Depends on the type of game I suppose, not all are high-speed button pressing fests. If you are terrible at high-APM games like Starcraft then it might be more due to hand-eye coordination skill than due to strategy skill, if you are also terrible at online chess then it might be due to strategy. Both hand-eye coordination and strategic thinking can be improved through practice though.

Performance in games like this is a child with many fathers. It's more likely that you underestimate the amount of work some people put into improving, and also underestimate the role of luck.