Is the Chomsky-hierarchy outdated?
In short: yes.

More particularly: Chomsky was one of the first to formalize a hierarchy relating languages, grammars, and automata. This insight is still very relevant and is taught in all intro courses on automata theory. However, the specific hierarchy Chomsky came up with and the names for the elements of the hierarchy aren't really significant anymore. We've since invented numerous formalisms which fall between levels of Chomsky's hierarchy, above it, or below it. And the names Chomsky used aren't particularly interesting, i.e. they aren't based on an interesting measure of complexity or anything, they're just numbers. Should mildly context sensitive languages be Type-1.5 or Type-1.7 or Type-1.3? Who cares. "Mildly context sensitive" is a much more informative name.

The Complexity Zoo is a bit different because it's full of all sorts of conditional equivalences and the like. A more modern hierarchy for automata theory wouldn't be linear (e.g., compare CFG vs PEG) but it would still have a well-known topology. To get a perspective on modern automata theory you should look at work on parser combinator libraries and some of the stuff on unification and type theory (though those both branch out far afield).