So if this group is opposed to Biocentrism and supports Anthropocentrism, doesn't that just make this a sort of Human Nationalist group?

Why would it? "Human" isn't a nationality. It's something much more fundamental.

I don't want to sound weird, but if intelligent alien life was discovered, wouldn't this group technically put the needs of humans first, believe that humans are number 1, and not favor cooperation with them?

It depends on the circumstances. That would be a false dichotomy if co-operation with an alien species was conducive to human interests.

If however an alien species came looking to exterminate or enslave us that would be a different matter. Either way its highly likely that within an alien society nationalism (or their closest equivalent of the term) would be as institutions, absurd, antiquated and as irrelevant as witch hunting or feudalism is to us today.