> nobody uses the old definition because it's no longer WW2

These are Cold War terms (post WW2). And for the Cold War era it makes sense to use the original meaning.

IMHO the term "3rd world country" shouldn't be used in the first place when talking about the time after the early 1990s though. It's misleading and the "modern" meaning comes with a hefty whiff of implied racism/colonialism.