You'll probably be interested in this post over at /r/badhistory by /u/anthropology_nerd.

The video in question is essentially parroting tropes from Guns, Germs, and Steel, which the linked post discusses directly, as does this section of our FAQs. The problem here is that Diamond is way off the mark when it comes to the origins of zoonotic diseases. Serious diseases originating from domesticated animals are actually in the minority. Measles almost certainly came from domesticated hoofstock (probably cows, maybe goats or sheep) and the flu possibly counts as well though we're sometimes n a "canary-in-the-coal-mine" scenario where our domesticated animals just get sick from new flu strains first and it would eventually hit us eventually anyhow.

Other major diseases are / were transmitted by wild species. Smallpox and tuberculosis both predate the domestication of any animal species. Smallpox likely originated as a rodentpox in Africa. Tuberculosis reached the New World via seals and / or sea lions (its Old World origins are more obscure since its so old there). Malaria is spread by mosquitos. The Black Death was spread by rats and their fleas. Cocoliztli, an devastating disease native to the New World that killed between 7 and 17 million people in Mexico during the 16th Century, seems to have been spread by mice. HIV comes from SIV (simian immunodeficiency virus) which infects wild primates and probably jumped to us through the bushmeat market (ebola is suspected of having reached humans by a similar means but that's not confirmed at this time as far as I'm aware).

Additionally, the Americas were hardly without their own host of nasty illness (cocoliztli being the worst, and thankfully we haven't been hit with a major epidemic of it since the 1570s). Europe just lucked out because, if a conquistador came down with cocoliztli and returned to Spain, he couldn't pass it on to anyone else.