A model that is similar to donations that I feel has not been fully explored is charging for cosmetic items. Reddit essentially does this now by allowing people to buy reddit gold, silver, or other awards.

This revenue model has turned out to be quite profitable in gaming and creates an experience where most people can use the software for free but a long tail of users spend lots of money to have icons next to their name or elsewhere on the site.

For chess you can imagine how this might work, for other software it is not always as clear.