His argument makes sense, but may be missing several factors (such as the plagues are not only caused by animal domestication). His argument closely parallels Jared Diamond's Guns, Germs, and Steel which has been refuted by many anthropologists and historians. See this post for more info. Colonization was a complex process, and cannot be be simply explained by plagues or technology. His arguments are reasonable to explain why there was no Ameripox, but shouldn't really be applied to explain American colonization.

He's basically parroting a lot of the arguments being made in Guns, Germs, and Steel, a book that has been picked to death both here and at /r/badhistory.

My biggest issue with the video is near the end, when he says that "the game of civilization has nothing to do with the players and everything to do with the map", which denies a lot of the cultural differences and motivations as well as human agency critical in the colonization of the Americas.

Hold on. When the Conquistadors arrived in Tenochitlan in 1519 the population was estimated at between 200k-300k. I'm having difficulty finding population stats for Cuzco, but the city was not small. For context the population of London in 1500 was between 50k-100k, the population of Paris in 1500 was about 200k and Venice between 100k-170k. He may be referring to the North Americans, where the population density was low, but in the south there were millions and millions of people. Many of these lived in cities.

Just as an aside there was a devastating disease that came from the new world, called Syphilis.

J.H. Elliott: Empires of the Atlantic World

I'd strongly recommend the work of David S. Jones, who presented a far-ranging critique of the notion that Native depopulation was solely (or even mainly) the result of a lack of immunity to epidemic diseases in a 2003 article in the William & Mary Quarterly.

Jones approached the problem from a medical point of view - his expertise is in medicine rather than history - and came to the conclusion that the "virgin soil epidemic" explanation espoused by scholars such as Jared Diamond and Alfred Crosby was based on many faulty assumptions about the nature of immunity. He argued that sociological factors associated with colonialism - such as warfare, malnutrition, and displacement - may have caused higher rates of disease, rather than the innate immunological vulnerability of indigenous people. What's more, the rate of depopulation seems to have varied greatly according to the specific circumstances of indigenous groups - whether they lived in highland or lowland areas, close to the coast or the interior, their specific genetic makeup, the nature of their contact with Europeans.

(One book that makes this connection between rates of mortality and specific circumstances is James Daschuk's Clearing the Plains, which shows that the supposed susceptibility of Canadian Native people to tuberculosis was in fact the result of government policies that left them chronically malnourished in the late 19th and early 20th centuries.)

In a more recent article on the subject in the edited collection Beyond Germs: Native Depopulation in North America, Jones explains the political implications of the "virgin soil epidemic" for our understanding of history. I think it's worth an extended quote:

When I first encountered the literature on the Columbian Encounter as a medical student, I was startled by the ubiquitous—and impossible—assertions of “no immunity.” Reading more, I found the work by scholars who emphasized contingency, as well as work in medical anthropology about social suffering and embodiment. When I returned to the medical literature on race, genetics, and immunology, I found more reasons to be skeptical of the simplistic claims made by Diamond and so many others. It became clear that virgin soil theory and its claims of “no immunity” had powerful and promiscuous appeal. They provided an alternative to human-centric histories, something that became increasingly attractive as environmental history rose to prominence. They shifted blame off Europeans and the Black Legend and onto morally neutral biohistorical forces. As Lawrence Summers, then president of Harvard University, described in 2004, “the vast majority of suffering that was visited on the Native American population as the Europeans came was not a plan or an attack, it was in many ways a coincidence.” The narratives simultaneously shifted blame away from the failings of Indian societies and onto their inexperienced immune systems, something that was simply the result of quirky geography. Virgin soil theory resonated with powerful narrative tropes, telling how virgin Indians yielded to potent European pathogens. By representing Indian mortality as the product of a unique historical-immunological moment—the collision of two long isolated populations—it created a buffer between the horrors of the past and our present. (p. 24)

The thing to remember is that this video is trying to explain a very specific thing; why didn't American diseases wipe out Europeans after 1492. It is not talking about Jared Diamond, colonization, or technology. So anyone talking about that stuff is just flogging their own biases. It is also a 10 minute video, so understand that some things may be glossed over.

As for your specific questions, I would like to clarify a few things. 1) There were large cities in the Americas, but not nearly as many as in all of Europe, North Africa, and Asia obviously. 2) You can't keep animals out of cities. (Any major city today will have rodent issues.) Eurasian communities likely had close contact with a greater number of animal species though. 3) There were other domesticated animals in the Americas. Dogs and guinea pigs certainly. Turkey and maybe a few other small birds. (I am curious as to why reindeer were semi-domesticated in Asia, but caribou were not in North America. The same with the peccary, which are related to pigs. That is a different issue though.) Basically though, no large draft animals.

The biggest thing the video left out is trade. The trade networks of the Americas were minuscule in comparison to those in Europe, Asia, and North Africa. The great empires of the Aztecs and the Incas were separated by an isthmus of jungle and swamps. The Aztecs were also isolated by deserts in the north and Incas were cut off from the Amazon tribes by the Andes. It wasn't that trade was impossible, but the lack of large ships and draft animals meant that the trade was harder and less profitable. That meant less travelers to spread the diseases that did appear. Conversely, domesticated animals and large ships helped to spread diseases around Eurasia. Not only were more people traveling, but a sick man on a horse can go much farther than one on foot. Large ships are also a great vector of disease transmission. They can carry infected humans as well as infected animals, like, say, plague rats. I wish trade had been included as a fourth part of the puzzle.

At best his is only half an answer.

He asks "why didn't the Europeans get sick". But he misses the answer despite being right on top of it. The answer is that they did. A lot. Repeatedly. Hundreds of millions of Europeans died from plagues and epidemic diseases. In fact, more Europeans died from such diseases than indigenous Americans. But these waves of diseases did not come primarily from the new world.

The real question is not why didn't Europeans get sick, they did get sick, a lot, as even he acknowledges. The real question is why was European civilization able to survive these onslaughts while native American civilizations imploded? And that comes down to their level of technology and their organization of their societies. Iron age, classical, and medieval societies in Europe had the ability to weather plagues and survive. In parts of Europe the black plague took nearly 80% of the population, yet it survived. It survived because it was built on systems of dry grain storage as the core food staple, it had a food surplus, it had the ability for individuals to grow more than enough food for their own survival without a lot of help, and it was reasonably well organized. The Americas was far more fragmented into smaller communities with a lower level of technology and less ability to weather dramatic upheavals over long periods. In many places in the Americas the death of huge percentages of the population resulted in reduced ability to bring in food (via hunting though also farming) which caused a downward spiral of viability for individual tribes and ultimately even for many of the larger settlements. In Europe a reduction of population initially meant more food for those who remained, and more work and money for them as well. In the Americas a reduction of population meant less food for everyone, which accelerated the decline.

If Europe had instead encountered a mirror image of itself, though with its own variants of endemic plagues, would they have merely wiped one another out? That's a possibility, but it seems more likely that they would experience horrible plagues and mass deaths but still stand.

Just important to remember that his videos are certainly simplified arguments due to time constraints and a desire to appeal to a wider audience.

I have a question here:

Wouldn't the transmission of diseases to Americans be due to the sheer number of carriers (most likely dormant) who came over and interacted with the American natives?

And conversely, there simply weren't huge numbers coming back until later, and at that time all the plagues had done their work and only resistant people remained?