If you think fighting games don't involve skill try beating an experienced Street Fighter 2 player having never played the game. When you lose, and lament that you 'simply haven't memorized the combos' go home and look them up. After you've realized that there's only one or two major combos to learn for each character in that game, come back and I promise you'll still lose. There's much more to it than that.
Most importantly, arcade games by their nature are finite. The limits of whatever storage medium used as well as the inability to rewrite or update them easily means that they exist in a vacuum. Once you've 'explored' the levels or found the 'secrets' they cease to be new. There are no more secrets. The strategy to beat single-player games never changes.
However the person you're playing against in a fighting game is always going to be different. Even if they play the same character as another person they will play them differently. They will have different skill levels and unique weak points to attack. No round of a fighting game is ever exactly the same. This is why fighting games are beautiful. They turn a static game into something timeless. There are still weekly Street Fighter 2 tournaments all over the world. When was the last time you competed with tens of other friends in say, Qbert 25+ years later?