Is it really Doom's frantic play that causes you to experience the pain of clenching and pounding keys? Perhaps in Doom, you noticed it more because the side effects of your playing was much more evident?
If you are trying too hard then you need to relax when playing as a priority. Anytime you clench or press keys too hard you gotta recognise it and stop immediately. It's kinda difficult to do at first but after a while you soon find the "zone" and gaming is so much easier.
You'll eventually find yourself sitting back watching the game while you're playing it and it doesn't matter if you lose a bit of what you perceive as your skills while learning to play this way 'cos in your current state of mind you'll actually be nowhere near your playing potential.
Calmness in gaming is the ultimate experience! Everyone should stay within their calm playing boundaries regardless of perceived experience or skill level outside it. Eventually those boundaries become much broader resulting in a much more enjoyable playing experience.