To me the only skill you keep between different games (especially different genres) is your eyes.
To most valuable skill of a gamer is its capacity to read to screen fast, and analyse the situation.
But if the best starcraft player was to play aginst a good street fighter 2 player (given starcraft player does not usually play street fighter), he would get his ass beaten in a blink.
So the question is not do you think you are a skilled player, but in wich games are you skilled, and how would you rate your skills ? IMO