The public game room has lots of general random topics, or you can create a private group and make your own challenges with any topics you like.
This is a personal/passion project of mine (and has gotten fairly popular these days). I'm actively working on improving the game, by adding category specific games, different game modes, etc.
I built an app based on that exact concept: http://thewikigame.com which has been running for many years, and is now quite popular.
The database of the site now contains a large record of millions of game plays of players trying to go from one Wikipedia link to another. See here for some interesting academic research that has been done on the site's dataset: https://docs.google.com/document/d/1jSGFRZYrJnlDUBhGbQrO9e-n...
I'm currently developing an app based on Gimbal: https://gimbal.com (made by Qualcomm).
My experience so far has been pretty good using their SDK (which works on iOS and Android) and their admin web interface, and the Gimbal devices themselves are not that expensive.
I'd be interested to hear the experiences of others using Gimbal..
This project is pretty great for using Flask on App Engine: https://github.com/gae-init/gae-init - I've been using it for a while now, and it's been smooth sailing. Also, it's actively maintained and continually improving.