I've just read through it properly, and, aside from saying "thou" instead of "you" and "wilt" instead of "will", I can't see anything at all archaic about the language. Formal, yes, but what's archaic about formal?

As for "O Man", unless someone envisages the song as being addressed to an individual, which is a bit unlikely, it has to mean humanity as a whole, male and female. Which is yet a third meaning of the word.

Logically if someone objects to Man for the species because it's also used for one of the genders, they should do the same about "Goose" or "Duck", for example. I've never heard anyone do that for some uunaccountable reason. But maybe it's a controversial topic between Geese and Ganders and Ducks and Drakes and so forth...