My speculation is, that something's happened, and mutants have lost their powers.
It'd explain why Logan is suddenly aging (and Professor X is still alive; so basically it's not 100 years later, and Wolverine's older, and Professor X dead by this time).
I think his bloody hands were another hint, that his healing factor wasn't kicking in.
And that's what he means by "the world's a different place... there's no more mutants..."