I bought my Lenovo y560 in 2013. I also played games on it and oneday the GPU overheated and the whole computer crashed. Luckily I still had a warranty, so I simply exchanged it for a new one. But I have learnt my lesson.
This laptop is simply not built for applications requiring too much processing. It has the hardware, but the cooling system falls far behind. Be extremely cautious when playing games. Always play on the lowest graphics settings (Especially games like Assassin's Creed and Far Cry, both of which is by Ubisoft and for some reason heats up your CPU like nothing else).
Also, before playing, go to windows power options and set the maximum processor speed to 90% or less. This will significantly reduce the heat your processor produces.
If you want, you can even go into your GPU settings and select the most basic graphical processing options.
Rather safe than sorry