For example, something similar to Synacor Challenge (https://challenge.synacor.com/) or the Advent of Code(https://adventofcode.com/), or CTF games in general.

Do uploaded games need to have an executable, or does itch allow uploading anything (like a binary file containing a puzzle which needs to be solved), as long as it's considered a game in a sense?

thats ok but for players who are not tech experts they might be confuse and wonder were the exe is for windows or DMG/APP for mac users.

You're welcome to upload any kind of file. If it isn't an executable for a specific platform then please don't tag it as such, it can cause issues when someone tries to access the project in our app.