basically you were doing it right. I do a lot of screensharing with games. You will get proper results when you run the game in window mode.

To enable window mode for LOL please go to the game settings and enable it there.

screensharing games also uses a lot of resources so maybe your computer could be just to "weak".

Let me know if you got better results in window mode.

It works fine for me with Portal 2, WARP, SWTOR, LOL, Diablo 3 etc.....

Moritz