"¡Ellos invitaron a todo el mundo!"

literally, it's "all the world" I think that should be accepted, my understanding is that saying "todo el mundo" is a hyperbolic way of saying "everyone" like here the person seems shocked at how many people were invited (hence the exclamation points) But I'm not a native speaker, so I could be wrong.

It's an idiomatic way of saying "everyone".

It does translate to "the whole world" too, but generally it's an idiom meaning "everybody".

Ellos invitan a todo el mundo.