Without getting too deep into this, I have a degree in psychology and have worked in behavioral health for the last ten years.
Based on research and experience, there is virtually no correlation between violent video games and violent activities. Some inherently violent people may play video games and decide to act them out, but that's no different from someone copying a violent movie or imitating violent music.
In short, playing Doom or anything else won't damage you mentally. If anything, many people have found video games to be therapeutic due to either increased cognitive stimulation, or simply working through PTSD.