Athletes get paid to play because people will pay to watch. It's not a matter of what's "fair," it's what's profitable. E-Sports can be commercially viable (like Korean Starcraft, as Aegix mentioned), but the games need a very large and dedicated following, and they need staying power, because it's not worth the effort to spend several years building up a league only to watch it die as the fanbase moves on to some shiny new game. The major spectator sports like baseball and football have been around for generation, so it's only natural that more people will pay to watch them.
In any case, I don't think Gal Civ would make a great E-sport simply because it's single player. It's not nearly as much fun watching people play side-by-side for a high score as it is watching them compete head-to-head, and getting a high score in Gal Civ seems to be more about end-game grinding than winning quickly, as far as I can tell.