I admit that I don't play many games, the only one I play at the moment is Left4Dead2 (though previous measurements when playing Counterstrike where similar).
All my testing show, in a highly scientific study of 2 computers, that playing Left4Dead2 in Linux (Fedora 20 and 21) uses less processor power, and less ram than playing in Windows 7(which both computers came with).
I don't have a program that tracks GPU usage, but tracking the temperature of the GPU's shows that they run cooler in Linux.
So using the same resolution, detail level, etc., I get a better frame-rate in Linux, and lower chance of network lag.
Over all power usage, tracked from the power-supplies, show that both of computer systems use less power in Linux, for the same over-all result, the frame-rate is marginally better in Linux.
All computers/OS's combinations have as few other programs running as possible, so firewalls, antivirus, and stuff are also disabled.
All computers/OS's combinations run with updates on, and the latest drivers drivers(official AMD Catalyst driver in Linux), etc.).
But as this is a tiny, unscientific study as always... YMMV.