Competition is not the focus of the game, its something you can do, if you want to. You don't "win" Gems of War by climbing to the top of the leaderboard, earning a bunch of trophies, etc. The closest you get to "winning" is getting all troops, ascending them, leveling them, and traiting them. Nobody else is forced to not obtain troops, ascend, level or trait them just because you did. Competing is, by in large, not the objective of gems of war. Again, at least now.
Many single player games have scores and leaderboards, and that does not make them competitive games. Tic-Tac-Toe you are in direct competition with another player - that is the whole point. Chess, yes, competitive, the direct objective is to win a game. Mario Party 8.. yeah, debatable on how actually "competitive" it may be, but most modes are what would be a "competitive" game. Jumping rope.. is an odd example, as you may or may not be actually comparing scores with another person. But take something like Pac-Man, you could just want to clear as many level as you can without dying, or you could be going for the highest score, but it is not a competitive game.