When I mentioned this to my doctors (I've had five or six now in the past six years), they all said that this is a common reaction when adrenaline kicks in and then lets down. Thus, I didn't worry about it to much. Aside from adjusting my mouse sensitivity and avoiding more intense types of matches (especially 1v1 StarCraft multiplayer), it didn't really impact my life--until a few years ago when it started happening even when I wasn't playing a game.
The shakes have been more frequent this past year in particular. They don't happen all of the time and usually only occur when I am holding up something (like a coffee mug or a phone) in my right hand. However, they also happen when I'm not holding anything and can now occur in both hands. Normally, I can "reset" by placing my hand(s) on a solid surface, waiting a moment, and trying again--but not always.
Such was the case today as I was trying to use my phone to scan a reading for one of my classes as a PDF. Despite "resetting" multiple times, I kept having to retake the scans because they were coming out too blurry from my shaking. Granted, I was a bit hungry, and I think that could have been a factor.
My most recent doctor reassured me like the previous ones that this is not likely to be a serious problem--just a common occurrence as some people get older. Still, she asked that I take note and keep her informed. Benign or not, I don't like it.