LLMs use the same type of "abstract thinking" process as humans. Which is why they can struggle with 6-digit multiplication (unlike computer code, very much like humans), but not with parsing out metaphors or describing what love is (unlike computer code, very much like humans). The capability profile of an LLM is amusingly humanlike.
Setting the bar for "AI" at "singularity" is a bit like setting requirements for "fusion" at "creating a star more powerful than the Sun". Very good for dismissing all existing fusion research, but not any good for actually understanding fusion.
If we had two humans, one with IQ 80 and another with IQ 120, we wouldn't say that one of them isn't "thinking". It's just that one of them is much worse at "thinking" than the other. Which is where a lot of LLMs are currently at. They are, for all intents and purposes, thinking. Are they any good at it though? Depends on what you want from them. Sometimes they're good enough, and sometimes they aren't.