I make reference to this post from Ángel Martin, the developer of so many ROMs that we love to use (the Sandmath series of ROMs have been a permanent plug in my HP41CL memory). It includes some of the programs and exercises created by Valentín. While we are always in search of interesting programs, I bet that you will like more the accompanying articles. These are also referenced in Ángel Martín's article.
As an appetizer of what you can see there, there is a chess program! Due to the size of the printout of a chess table and the memory requirements, Valentin decided to settle on a 5x5 net instead of the standard 8x8 - but it is extremely interesting! The post provides the the manual that describes how to play it. It does not check the legality of your moves - but it does calculate its moves! Do not expect a fantastic performance, but with 50 times the speed of the original, it may amount to something.
Normally, it would require either fill in the program by hand (listing provided) or by barcodes (it requires to have the old HP41 barcode), but you don't need that if you have an HP41CL: you can upload the module with the seral cable and your computer!!