Another reason for making a game completely free (of payments, advertisement, sold user data, and so on) is ones portfolio/reputation. Having a good piece of work on his/her portfolio could give a good impression to potential employers, clients (e. g. contract work), or investors. The Android App Timely is for all I know a good example, since the company was bought after releasing this app (without any previous releases). Another one is Öffi, which is developed by a freelancing developer.
Some projects are completely free and the developers do it just because they love coding cool stuff.
A developer could also aim to get some media coverage by making a game related to a hot topic. An example would be "Abbruch Bayer" (which translates to something like "Bavaria demolition", in contrast to "Aufbruch Bayern"/"upswing Bavaria", the original game made by a political party about some numbers and values of Bavaria). Sadly, the linked article is only available in german, since the covered topic only has a local significance.
These are reasons a person, team or company could consider, but there are much less games (and applications) release with this intent, instead of "free" ones with some kind of monetization.