Just to add to this, after QA by me I was able to get it to fix all its mistakes, of which it had many. (Besides freezing, it didn't treat castling rules correctly, allowing castling out of and through check.) It was also able to add play by the computer and I could get dragging the pieces working on both desktop and mobile, though it took a lot of back and forth. The polished version of the game is now at: https://taonexus.com/chess.html
So the answer to the titular question is "yes, ChatGPT can make a complete chess game" in 2025 - with a lot of QA by a human in the loop!
https://chatgpt.com/share/67b5f635-ac40-800b-99bf-026e4b0b97...
you can see a copy of the game here, as written by ChatGPT in one shot:
https://taonexus.com/publicfiles/feb2025/chess.html