I'll throw in an answer from a different angle: social deduction games can be incredibly rules-light while still maintaining a lot of complexity. Resistance, for example, has not too many more rules than Go, but games can get deeply complex as players try to figure out who the spies are.
The big difference is of course that the complexity offered by something like Resistance is the product of imperfect information and willful deception, which means that a good ability to read people (or conversely, to lie) can be at least as important as strategic mastery.
Scheduling would not be fine; under HIPAA "provision of healthcare" is considered PHI, so knowing that person x had their care at a certain time and place would be a problem.