If you use the BGE to make a game and distribute the .exe along with the blends for a contest, if you win money from the contest, will it be breaking the GPL?
The short answer, no, GPL does not generally prevent you from selling or making money from the software. The only issue I’ve heard about here is that if you want your game to be closed source, it may need to be blenderplayer + file and not a single exe
You can make money with GPL software.