I played some Battlefield and Tomb Raider (2013). Both played well on the monitor. The input lag and response time of this monitor are good for an IPS panel. (but of course not as good as TN). For casual gaming, this is a fine monitor.
In terms of performance the 650m can't handle the latest games at 1440p so I lowered the Anti-Aliasing and I lowered the resolution to 1080p and graphics mostly medium (and some low) settings. 1080p on 1440p looks worse than 1080p on a 1080p screen but it's still decent looking and didn't spoil the fun. It's in my opinion definitely not as bad as people make it seem.
Your GTX680 can probably run games between 40-60 FPS at 1440p, and when lowering graphics and anti-aliasing even higher.