The very simple answer to this question is no. War crime and genocide are both legal rather than moral terms (although they are frequently used in both contexts).
Genocide has a systematic element to it absent from a single incident such as Dresden.
A war crime could technically be argued according to the Laws of War: Laws and Customs of War on Land (Hague IV); 18 October 1907 article 27 "...all necessary steps must be taken to spare, as far as possible, buildings dedicated to religion, art, science, or charitable purposes, historic monuments, hospitals, and places where the sick and wounded are collected...". No such efforts were made in the case of Dresden, the aerial bombardment was targeted at a city center well know for its cultural and historic value. Donald Bloxham, Gregory H. Stanton and Jörg Friedrich are all notable persons who argue that Dresden was a war crime, they are however a minority.
Most historians I've read argue that Dresden was immoral but not per se a war crime as the rules of war in play at the time had not been updated since 1907 and therefore a legal conviction would have been difficult.
I'm only going to address the issue of aerial bombardment because I think it'd be very difficult to construe Allied bombing of cities in WW2 as genocide.
The main issue with considering whether actions in WW2 were war crimes is that in many ways, modern ways of thinking about war crimes exist in response to the horrors of WW2.
During WW2, there was no international agreement definitively defining the aerial bombardment of civilian populations as a war crime. The Hague Convention of 1907, Article 25 specifies:
The attack or bombardment, by whatever means, of towns, villages, dwellings, or buildings which are undefended is prohibited.
The Hague Convention of 1907 is important because it was considered a formulation of the rules of war at the time, as the The Nuremberg Tribunal said, it was "recognized by all civilised nations" and "declaratory of the laws and customs of war which are referred to in Article 6 (b) of the [International Military Tribunal] Charter."
Notice the qualifier in Article 25, "which are undefended," appearing to allow that such bombardment is allowable under circumstances where the town is defended.
This does NOT necessarily mean that the bombing of Dresden was not a war crime. For instance, genocide as a word wasn't even coined until 1944, much less codified as a crime. Yet Nazi leaders were charged with genocide at the Nuremberg Tribunal.
Indeed, there may be ex post facto issues -- it seems unjust to charge someone with a crime if they couldn't look the crime up in the books and didn't have the expectation they'd be punished. But at the same time, international law has never been beholden to the positivist view that the law is limited to that which is written down or issued by an authority.
If performed today, bombings like Dresden, Hiroshima, and Nagasaki would most likely be war crimes.
For instance, Protocol I adopted in 1977, articles 51-54, protect civilians, civilian objects, cultural objects and places of worship, and objects necessary for survival (like farms and water supplies). For instance, from Article 52:
Civilian objects shall not be the object of attack or of reprisals. Civilian objects are all objects which are not military objectives as defined in paragraph 2.
Attacks shall be limited strictly to military objectives. In so far as objects are concerned, military objectives are limited to those objects which by their nature, location, purpose or use make an effective contribution to military action and whose total or partial destruction, capture or neutralization, in the circumstances ruling at the time, offers a definite military advantage.
Similarly, the Rome Statute of the International Criminal Court. In Article 8(b)(iv)-(v), defining other serious violations of the laws of international conflict that are war crimes, specifies that violations include:
(iv) Intentionally launching an attack in the knowledge that such attack will cause incidental loss of life or injury to civilians or damage to civilian objects or widespread, long-term and severe damage to the natural environment which would be clearly excessive in relation to the concrete and direct overall military advantage anticipated;
(v) Attacking or bombarding, by whatever means, towns, villages, dwellings or buildings which are undefended and which are not military objectives;
Therefore, whether or not Dresden was a war crime depends on how you think about the law
If you believe in an essentially positivist view, Dresden could not have been a war crime, because the law is simply determined by social fact (like the social fact that the Hague Convention of 1907 allowed aerial bombardment of defended civilian populations, and the social fact that after WW2, international agreements prohibited it) end of discussion.
If you subscribe to a jurisprudential philosophy in the tradition of natural law, then you might say that the nature and authority of law depend on the consistency of human law with higher, unwritten moral principles. The indiscriminate bombing of civilian populations, you might argue, violates those principles, and are always war crimes, whether there is a law or not, and the fact that such actions will not be prosecuted is immaterial to the fact that such actions deserve to be prosecuted.
This was not a warcrime as understood at the time. /u/Spot_Pilgrim further in the thread gives a very good definition of what was considered to be a warcrime and what wasn't. Essentially, if you had a town or city that was a political, logistical or military manufacturing hub, it would have been fair game.
Stalin was concerned that the Germans were regrouping. If the war was "won" then the Germans should have surrendered. They had not. The allies had already been attacked during Ardennes Counter-offensive authorised by a Hitler that wanted to press for a negotiated rather than an unconditional surrender. There was a plan to build a defensive line on the Elbe, and the concept of regrouping in the South of Germany was suspected, even if the plans were not known in detail. Btw, ironically the Allies had less access to German High Command messages towards the end of the war, as they were using landlines rather than radio, so the Allies did not know that the Germans were about to cave.
The attack on Dresden seems hard in retrospect, but in that time there were attacks on places like Darmstadt, Kassel, Pforzheim and Wuerzburg. Many as destructive, if not more so (in Pforzheim, 1/6th of its population were killed and 83% of its population destroyed in one night, a couple of weeks after Dresden). The difference is that these latter cities were in the Federal Republic after the war so less mythologising and they weren't so pretty.
Dresden was a beautiful city but it had not been demilitarised or declared to be "Open". On January 1, 1945 General Guderian declared Dresden to be a Verteidigungsberich or "Military Defence Point". Essentially, it was expected to defend itself to the end with no surrender and was to become part of a defensive line on the Elbe.
First, the war was not over and no ceasefire was in place and Hitler was very much still alive. You do not take your foot off the pedal because the enemy is losing and there had already been losses due to the Ardennes counter offensive.
Secondly, in WW2, precision bombing didn't work very well. There were a few exceptions involving low level attacks, but these were very limited and the losses were high (the Dambusters being an example). Most bombing was area by that point of the war. You had particular targets which would be marked by the Pathfinders but the dropped bombs could be anywhere in several kilometres. Once the initial bombs had dropped secondary fires would quickly mask the real aim points. In any case, in common with many German cities, the main station and the goods yards were fairly central.
Next, the city contained (according to the German High Command's own handbook) identified 127 companies that were directly supplying the military and this does not count smaller workshops that supplied them. Civilian factories were repurposed so that a company involved in machine manufacture for confectioners switched to making torpedo parts for the navy. Other companies made field telephones, the afore mentioned bomb sights, steering elements and so on. Note that as Dresden jealously guarded its Judenfrei status, they were marched five miles to and from the factories. As armaments Jews they lived better than others but ideology was prevailing over common sense and there had been a decision to eliminate the remainder.
It should also be mentioned that whilst the Nazi officials running Dresden and the military had ensured their own survival in case of an attack, the fact that it had not been bombed earlier encouraged them to economise on protecting the rest of the population. Other cities tried rather better to protect their population.
It should also be noted that after the attack, the Germans made full use of existing slave labourers, both those in concentration camps and Allied POWs like Vonnegut to collect bodies and repair the damage.
Finally, the level of damage was a myth sanctioned by Goebels (a zero was added to initial estimates and the military / industrial connections concealed. It was perpetuated under the DDR (which helped to mask the tens of thousands of women raped by the advancing Red Army) and finally written up by a Holocaust apologist (Irving) and adopted in more recent times by the ultra-right wing. It is only after the end of the DDR that the matter could be dispassionately reexamined.
The book upon which a lot of stories were based is Der Tod von Dresden by Axel Rodenberger. He grossly and unprofessionally overestimated casualties by over a factor of ten, perhaps using the faked Nazi data. The next was Die Unbesiegbare Stadt by Max Seydewitz (1955) which was backed by the DDR regime. Then there was The Destruction of Dresden by David Irving (1963).
My source is Dresden: TUESDAY 13 FEBRUARY 1945 by Frederick Taylor (2004) which dismantles a lot of the myths from the number of casualties, the so-called massacre on the "Elbe Meadows" and the nature of the targets.
Another source in German: Report of the German Historical Commission of the number of casualties from the air attack on the city of Dresden on 13/14 February 1945, published by the Regional Capital, Dresden Retrieved from the city's web site on 21 March 2014.
Can I ask a side question of why was the Bombing of Dresden different from other bombings of civilian targets at the time? I'm not trying to make a point, I really just don't know much about it.
Does anyone have an accurate number of casualties? I've heard anywhere from 30,000 to 800,000