Dimensionality is about either having more than one kind of test in your game (as Wii Sports does, with many different events) or multiple tactics that can be used to solve one test. Strong dimensionality means that there is no dominant tactic, that every action implies a trade-off in another direction, and that it all makes a certain balanced sense.
Aiming for at least three dimensions that counterbalance each other usually gives the player plenty to play with. Four is fine, even five. However if your game has seven dimensions then it’s probably too complicated. Whereas if it only has one, there is no opportunity to balance anything.