Subbuteo soccer (well "football" to me as I'm from England) was arguably the ultimate dexterity sports game. It spawned a number of siblings - rugby, cricket and angling included.
In Subbuteo rugby, you flick small plastic players on a cloth pitch to take possession of a small plastic rugby ball (similar shape to an American football). The rules included most elements of the sport of rugby - lineouts, scrums, offside, tries, kicked goals, etc.
The game also included a number of specialized plastic components: figures which swung their kicking legs to "kick" the ball over the plastic goal posts; a plastic wedge to "loft" the ball; and a large rugby-ball shaped randomizing devise into which the smaller ball was dropped to decide scrums.