Is the "us" in "all that will be left is us" correct usage?

I can't really comment on the correct grammar, but the full quote makes more sense:

"They made us too smart, too quick, and too many. We are suffering for the mistakes they made because when the end comes all that will be left is us. That's why they hate us."

Us is not really being used as us traditionally but a placeholder for the entire concept of AI because there really isn't another word for it. I believe the grammar is bent for the purpose of emphasis. look at this pattern:

They made us
All that will be left is us
they hate us

it forms a pattern that makes more sense if spoken with dramatic inflection.

We is a nominative pronoun, while us is the objective (accusative) case of we.

In "X is us", X is the subject, and us is the object (hence the objective case). Compare that with "We are X", where we is the subject (hence the nominative case), and X is the object.

On a more general note, see this answer to a related question.