Competitive gaming is as much a sport as chess imo, but I wouldn't call either an athlete. People are even arguing whether or not race drivers are athletes (they truly are imo, most people have no idea how much physical strain is put on the body during a race).
Playing video games in and on itself is not any form of athleticism, agreed? Then by extension; I would argue that people who happen to compete in said video games aren't athletes, a simple change of setting does nothing to change that (a ferocious Starcraft match on LAN vs one in a contest).
E-gaming has been classified as sports in more and more places, and that's fine, sports as an expression does not imply that there is a heavy element of athleticism involved, the term "athlete" does not cover e-gaming competitors in my honest opinion.
Bottom line for me; sportsman: granted, why not? Athlete: no, not as such, there is no proper grounds for calling these competitors athletes.