howling dogs and Impostor Syndrome both contain puzzles that I can’t describe without spoiling them, so I’m going to describe them under a spoiler.
They each contain giant fields of links where only one or two links will take you to the Good End, though that’s a bit of a reductive description anyway. In howling dogs all the wrong choices had an anodyne response that took you back to the original link-field, and there was a link that let you move on (and thus fail the puzzle); there were so many anodyne responses that no one was likely to find the true one by link-spamming them all. In fact, I didn’t realize there was a puzzle until I saw it mentioned in a review. In Impostor Syndrome choosing a wrong link just takes you straight to the Bad End.
My advice is not to try one of these puzzles unless you have an interesting way of varying the implementation (though don’t let me stop you from thinking of one!); they’re much less effective when the freshness has worn off. And it’s significant that neither of these is really a puzzle game; getting what I not entirely seriously called the Bad End is not like losing or getting stuck in a puzzly game.
You can definitely do code-based puzzles in a choice game. Meanwhile (which is a book) does this. It also has an optimization puzzle which combines with that. [On preview, zarf mentioned this, and also the point about S&W in the next paragraph]
Puzzles that don’t work in choice-based formats; I’m surprised Carolyn cited Spider & Web because its most famous puzzle, which may be the most famous puzzle in post-Infocom IF, is commonly cited as one that wouldn’t work without the parser (I agree). My Faithful Companion (one of the parser-based Best Puzzle nominees!) wouldn’t work in a choice-based format either; the central mechanism requires that the player be able to perform a wide range of actions, and… well, mild spoiler
the nominated puzzle requires that you think of doing something which it’s implicit that you can do, and when you think of it it’ll be obvious that you ought to be able to do it (or try it), but if it was presented as an option that would spoil much of the puzzle. More details here but it’s a very short game, why not try it?