Eh, I decided to not play it. There is no option to minimize the game without ending it, and I cannot just play the game without also checking on things online.
the windows button on your keyboard minimizes most games that don't have the option built in. i haven't played league of legends, so i can't say i've tested this with that game.
There is a tiny option button in the lower right hand corner. It is the 3rd of the 4 buttons above the right top of the map. Hit video setting and then Windowed mode.