[arayh]

Would it make sense to classify them as irregular expressions?

[coldtea]

Maybe, but there's an actual hierarchy of languages (or grammars) based on expression capability -- regular languages are at the base.

There's (in more powerful order): context-free, context-sensitive, recursively-enumerable.

https://en.wikipedia.org/wiki/Chomsky_hierarchy

[empath75]

I think most people call them extended regular expressions.