Mac Minis are cheap, however they lack power at their price point for professional work. $500 for a dual core with a base clock of 1.4GHz, turbo of 2.7GHz, 4GB of RAM, and a 5400RPM drive? Unfortunately that's simply not going to cut it. When you move up the to the $700 price, you get a higher base clock, 400MHz of turbo boost overhead, 8GB of RAM, and a (larger) 5400RPM drive. And at $1000? You still have a dual core. You still only have 8GB of RAM. The only added feature to it is a Fusion drive in lieu of the 5400RPM drive, which is much much better than the full mechanical drive, however the rest of the specs simply still do not cut it. If it were for light work then that would be fine; but it's not. Game developing can get to be very strenuous on a system. Software compatibility shouldn't be an issue as bootcamp is available... but to run both games and game develop you're going to want a dedicated GPU. Which puts you in the range of the iMacs, Macbook Pros, and Mac Pros.
Depending on what you're game devving for, how intensive the engines are going to be (is it going to be as intensive as Void? or is it going to use Undertale's engine?), and how strenuous the games you want to play are going to be could end up with an entirely different recommendation of say, splitting the budget between a Mac, and a gaming computer. It can absolutely be done; it would not be optimal but it can be done.