When designing a competitive game, you have to choose solid core mechanics. To nail down the mechanics it helps to think about the skills a top player must have. Imagine a world championship of your game. What skills must the winner have? I came up with the following.
One skill is bargaining. Board games like Settlers of Catan or Diplomacy require this. To win the game you must successfully negotiate various deals with your competitors.
Another skill would be predicting your opponent. The classic example is rock-paper-scissors. If you can precisely predict what your opponent will do next, you easily win every match. Such games usually are played in simultaneous turns. However, fast real time also work. For example, Street Fighter and similar games. David Sirlin has a lot to say about this.
The next skill is thinking ahead. Chess is the classic game here. AI can beat every human player these days by thinking ahead much further. This skill might also be called strategy, but that would be less precise.
Another skill is estimating probabilities. For example, Poker requires this to win. It is fascinating how bad humans are with this. It requires the player to roughly estimate the probabilities of game situations and adapt them to complexities. A good Poker player knows his odds with an open-ended straight draw, but he will further adapt it to pot size, psychology of opponents, table position, and other factors.
Then there is memorizing game history. Basically, to win you need to remember everything which happen in the game. Counting cards in Black Jack would be an example. However, in many card games it pays of to memorize previous tricks.
A similar skill is memorizing lots of facts beforehand. For example, to win in League of Legends you need to know 100 heroes with their special tricks. A good player of Magic the Gathering or Pokemon also knows lots of facts.
Another skill is dexterity. Rarely necessary in board games, it becomes more important for physical sports.
Then there are reflexes. Quake and other first person shooters require this. Most physical sports as well, because a ball usually moves faster than your brain can make a conscious decision.
Finally, I list endurance. The classic example would be Marathon. However, most physical sports demand some endurance from the athlete. In digital games the grinding might fall into this category.
Note that most games are not purely won through one skill alone. It requires a mixture of skills. So when designing a game, I would recommend to order these skills, so you know which are core mechanics and which should play no role.