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So, the sport/game here is defined as having some moving element, which you're tasked with propelling through obstacles to some kind of capture point, which is the goal. Right?
I'm guessing the answer is a single electron in a series of semiconducting nanostructures at near-absolute zero, with a quantum dot as the hole. I'd assume there's some sort of way you could impart controlled momentum to the "ball" with a laser, and some way to measure where it is afterwards. Smaller than that, and we have pretty little control over what matter does.
Interference patterns as a strategic element could be kind of interesting. And, you'd have to relax any rules about waiting for the ball to stop, since by the uncertainty principle that can't happen.
The cooling reqiurement is a huge practical challenge - you'd need temps within a fraction of a degree of absolute zero to minimize thermal noise that would basically make your "ball" bounce around randomly like its constantly hitting invisible bumpers.
Yep. Hopefully the dilution refrigerators they use for quantum computers would work. Electrons are also easier than more substantial particles to keep still IIRC.
In hindsight, it's obvious that the "club" should be an electrostatic field modulated in the RF range, not a laser. We've been carefully knocking electrons around with fields since Faraday, after all. The hardest part would be to incorporate a grid of minimally-invasive single electron detectors. And maybe the more whimsical obstacles, if you really want an electron windmill.