If you want to play games without using the mouse, I highly recommend using a hands-free mouse. I personally use [SmartNav](http://superuser.com/a/435266/116475) on Windows (also available on Mac but I haven't tried it there): I use it all the time when using the computer and it works just as good as a mouse. To perform mouse clicks I use the dwell clicking software provided by SmartNAV. 

With this, you should be able to play any mouse-only games if it's okay to click is ~0.5 second instead of clicking immediately. Also, if you need to perform another mouseclick than left-click, you have to first click in the dwell clicking software to indicate that the next mouseclick be another type. You could also define a voice command to take care of that, which I haven't done yet (because SmartNav dwell kicking software cannot be used with shortcuts, and Sikuli has issue working with the SmartNAV dwell clicking software's window, so you probably would have to switch to another dwell clicking software) but I really should one day. So far I have been waiting for SmartNav to add shortcuts, a feature that I asked for years ago and should stop waiting for even though they say they would add at some point.

Now if you need to use the keyboard, the best hands-free solution I am aware of is defining voice commands in Dragon NaturallySpeaking Professional (if not Professional you won't be able to define advanced voice commands). A [Dragon Gaming Speech Pack](http://www.nuance.com/for-individuals/by-product/dragon-for-pc/add-ons/index.htm) (non free, Windows) is available, which I haven't tried, but since most commands in your case would be keyboard stokes should be straightforward. One issue is that there is a small recognition lag (say 0.5 to 1 second), which you should be able to reduce a beat by switching to the command mode:

![enter image description here][1]

So any game that would be okay to play with given those conditions could be played without any mouse and keyboard. I would say that many RTS/board/turn-based games should be okay, but most FPS games won't work well.

PS: If you investigate this solution, please let me know how it goes, I've always wanted to try more seriously hands-free gaming but haven't found the time yet.

  [1]: https://i.sstatic.net/tMgsh.png