I don’t know the answer for the last part, but chess has many, something like 20, although this doesn’t mean people always recall the more obscure ones. Chess is hard to master, but I wouldn’t say it is particularly hard to learn.

A Starcraft 2 player not only knows 50+ rules and has a firm grasp of what each unit can do (~90 different units I guess). A experienced Dota 2 player has played and knows all the rules of about 100 characters, with 3–8 skills each, and 100+ purchasable items. These, of course, take quite some time to learn and a lot of interest by the player in doing so. My point here is that, given time and interest, the upper bound can be quite high.