If this is a natural world, there would be no sport that does not already include the influence of TK within the game. We wouldn't be looking at how to fit TK into a game, but should be thinking of how sport would exist in the ambient background of TK.
If there were a significant change in the availability or power of TK, there would be disruptions within the sport.
We see the same thing today, not with TK, but with steroid medication and tests for gender specific hormones. It echos in the discussions over trans-women participating in women's sports. There is a disruption -- in pharmacology or social values -- and the disruption impacts sport and games.
In your world, sports would have included TK. If the stakes for success are low, the rules would be "soft" and not need to be enforced. In our world, who really cares if one kid is getting growth hormones for some condition, and it helps them hit better? In a sand-lot baseball game, no one cares. The sport is about the play, the team, and friendly competition. Teams are fluid. If one player is noticeably better, he will be switched over time between teams. In your world, TK abilities would just be one more aspect of athletics. A player might be a slow runner, have bad eyesight, but help the team with TK abilities. Another play may be weak at TK, but runs faster. The mix of abilities would naturally work together on a team.
If the stakes are high, the player's play probably wouldn't be changed, but the influence of the crowd, the promoters, the advertisers, and the gamblers would be valid points of concern. High stakes means many more stake holders. We have the same problems now, with players being bribed to shave points, horse trainers drugging racehorses, and athletes (and athletic sponsors) trying to game the drug-testing procedures.
With high stakes, it is a story of influence and corruption, just as it is today. TK is one more pathway for corruption to be applied, but it isn't a new problem. It is only a new vector.
If this is critical to your story, I would suggest simply adding a line that everyone played fair. If you want to drive it into the plot, it would be the same sort of investigation and exposure plot you would write about this works, with some TK bling.