I mean I would definitely describe the way it processes things as a thought process. Researchers have had to fine tune the algorithm to find something that will simulate the human thought process enough that it produces text that we can also fundamentally understand as (human) communication. In doing so it is dealing with high level concepts in a fluid way like ourselves.

To say "stop anthropomorphizing" this algorithm is dumb because the entire intent is to mimic the way humans communicate on the internet.

It might not have a sense of self, it might be unable to dynamically change... But to me it's at least a rudimentary capture of the thought processes of the brain. It has intelligence in the way we describe intelligence, but nothing more.