You have to run the game in Borderless window mode (not fullscreen, it will look like fullscreen though), then you can switch between screens without alt tabbing. To change to borderless window mode, it usually is in the video/graphics option menu. It works 100% in League of Legends as I do that as well. Some games do not have a borderless window mode, and unfortunately you will have to alt-tab to switch between monitors. I think Diablo 3 has the option as well, but I'm not too sure. Hope I helped.