Asking why something is so obscure seems an odd question, historically. It both assigns some perception of how well known an event should be, and then gauges a current level of perception that is not in accord with that expectation. After all, Emperor Probus of the Roman Empire is certainly not well-known -- but would we expect him to be?

Is the Battle of Mukden obscure? Anecdotally, I would agree, at least in countries that aren't Japan or Russia (Edit: or China, see /u/Keyilan's great note below). Is it more obscure, however, than other pre-WWI historical events? I would suppose the only reason we might think the Battle of Mukden should be more well-known is its status as the "largest single military operation in the history of mankind up to this point" -- but with WWI following so quickly on its heels, is it any surprise that this battle, and the Russo-Japanese war more broadly, gets buried?

So on the whole, I think the judgment of why an event isn't better-known an odd one, and probably nigh-impossible to actually judge in this case. Still, I'll endeavour to answer your latter questions, because most certainly -- at the time, the Battle of Mukden was quite well-covered.

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I'll give you the battle as described by the New York Times. If you are subscribed to the Times, and have any interest in history, I would extremely recommend you check out their TimesMachine. 150 years of top-tier journalism, easily searchable, seen on the page as it was published.

Prior to Mukden, the Times -- and many other newspapers -- had long been reporting on the Russo-Japanese war. Not all of this reporting was front-page material, but it can help to give a sense of the journalistic perception of the war prior to Mukden.

On Jan. 8, 1905, for example, the Times reports on the meeting of Gens. Nogi and Stoessel following the surrender of Port Arthur. The front-page headline reads "Nogi and Stoessel in Duel of Courtesy." The text describes how "both generals [...] mutually praised each other and their officers for their bravery" and speaking of the death of his sons, Gen. Nogi explains "I am glad that the sacrifices of my sons' lives was [sp] in the capture of such important positions, as I feel their sacrifices were not in vain." I'll not go into more detail here, since it is a bit tangential to your questions about Mukden, but I hope it does give you a sense that the Russo-Japanese war was fairly widely reported on, and given much of the importance it deserved in Western media.

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Now, moving on to the Battle of Mukden. We do see some aspects of early 20th Century journalism that stand in stark contrast to the blindingly fast news cycle we are familiar with today. The first mention of the battle comes on Feb. 24, in an article headlined "Rumors of Battle Persist." The article is brief and sourced in St. Petersburg, and describes the strained evidence relied on to make the judgment: "A second day has passed without dispatches from Gen. Kuropatkin having been given out," "special dispatches [...] mutilated [...] [as they] pass the censor" all "portend the imminence of extensive operations."

The next day includes the front-page headline, "Battle in Mountains; Russians driven Back." There's not an indication -- yet -- of just how bloody the battle will become, but certainly it is meriting attention. On Feb. 28, the front page reports "Oyama's Troops Cross Sha River," and we get a sense of the "desperate fighting" going on.

By March 1, the Times is reporting (again, on the front page) that "Big Battle Raging; Russians in Danger"; the following day, while information is largely censored, the Times relies on that fact to report (also on the front page) "Disaster to Army Feared in Russia."

There is continued reporting on Mukden, by March 5, we begin to get a sense of the battle's carnage: a front page headline blares "Russians Afraid Army is Crushed," and mentions "Japanese Casualties up to Friday Said to have Numbered 40,000 and Russians 30,000." The numbers keep climbing on March 6, the Times reports on the "teriffic losses, of which the total, on both sides, is estimated at 100,000."

On March 8, finally, at the top-left of A1, the Times reports "Russians Admit Mukden is Lost," and that the "Slaughter is Appalling." On the 10th, again on the Front Page, "Oyama Surrounds 200,000 Russians [...] The Slaughter Goes On."

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I'll not go into further detail about post-Mukden reporting, though it is similarly abundant. And while this has not consisted of personal accounts or photographic resources, I hope I have made clear that Mukden was not obscure, in any way, at the time. It was given the importance it rightfully deserved. Any obscurity will have been introduced in the century since, as its events grew over-shadowed by the even greater slaughters yet to come.