Hmmmmm.

Perhaps Zhodani sports have an additional purpose over and above the usual ones, in that they are used as one of the many ways to monitor proles for evidence of active psionics use? If a particular team/player beats the odds time and again, yet seems no better than average when assessed individually, then he/she is tested for psionics.

I think actual psionic games would be played mostly by intendents. This would be designed to show off each of the psionic talents, in two major facets, those of strength and precision. Since (as has been pointed out) possession of more than one talent is extremely rare (even among Zhodani), these would likely be team games. For example, I imagine something like the 3-D zero G combat game that is the major focus of activity in the novel Ender's Game. Each team would have a telepath (to probe the enemy's strategy), a teleport (a "flanker" who can pop behind/into enemy formations), one or more TKs (to help move group members about and also deflect incoming enemies) and perhaps a team captain with a Special talent that allows creation of a gestalt mind.

And - of course - these teams become Consular Guard Commando units in wartime. :P