I built a "word game engine" using a mix of AI, embeddings, wikidata, some bigram sources, wordnet, and a few others. I used all this to train a huge matrix of word associations. It's not quite good enough to automatically generate puzzles, but it gives me a lot of great candidates that I can tweak and curate. All the puzzles on the site are hand-picked and partially designed by me.
I think some of these chain puzzles are pretty neat. See if you can figure some of them out on hard mode (no hints).
I also built a clone of NYT Connections [1] using the same word engine.