Control Games running on Windows over network (and use ESC key)

I have one (Windows 8.1) PC set up for gaming only, and I can control that for the most part using VNC from Linux. The problem is however that controling the mouse in games (Tested using Dragon Age: Origins and Deus Ex: Human Revolution) moves the mouse in 'blocks'. Instead of smoothly moving the mouse like on the desktop, it behaves as if there was a 'move camera 3cm to the left/right/up/down' command. How could I make the mouse move smoothly?
My second question would be why the ESC key does not work? I assume it is some sort of 'security' feature, but I kinda need it for menus to work (Win+X also does not work... ). Is there something I can do here?
The entire point of this is to use my Linux Laptop as a controller. I am using VNC currently as that was the easiest to set up, however I am open to using other programs (remember, they do not necessarily have to steam video to my laptop, just allow me to control the game running on the other computer).
Best Answer
Steam has in-home streaming and only requires steam on both computers. You can add non-steam games. I know from personal experience that non-steam games that launch with the steam overlay enabled can stream so your friends can watch you play: when they enabled the feature, I had a friend send a request and successfully connect and view my game while I was playing Diablo3.
I expect the same is true for remote gaming, but I am not certain
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