Consider the case of Kevin Garnett. Because he did so poorly on his SAT's that college made no sense, he went directly from high school to the NBA. Yet while he was in the NBA he was one of the greatest defensive players of all time. He had the physical tools that players need to excel: height, speed, leaping ability, gross motor and fine motor skills. But lots of players have those and don't become all-timers. KG was known for perceiving angles and positioning, seeing how one small change in his positioning would affect not only his opponent, but the movement of the other players on the floor. Lebron has this ability as well, to notice and exploit what an opposing player is doing at a very small level. It is strongly related to "seeing the floor," though not quite the same. What observers call "anticipation" is sometimes this automatic spatial reasoning, though there is another sort of anticipation related to memory.
All basketball players must have some of this; not all are exceptional. Some rely on physical skills almost entirely.
So the SAT's don't pick this up, or at least not in isolation, though it is clearly an intellectual skill. I don't think schools pick up on this very well either. We all knew guys in school who could figure out everything about engines but had trouble passing classes. School and SAT's require that you be able to translate this in and out of written symbols to demonstrate the skill. If you don't have the skill with letters and symbols, your ability will go unrecognised as far as academics are concerned. Engineering students often have both. That is necessary in order to use the spatial skill with others, drawing up plans, following procedures. I don't know if there are good ways of measuring spatial intelligence in isolation.
It is used in a lot of outside-of-school skills. Some females have it, but I think fewer than males. With the ridiculously low sample size of exceptional basketball players, most of whom are black, I wonder if there is not some school unfairness for them as well. Some, at least, have this intellectual ability but do poorly on the tests and in the classroom. I don't know the WAIS well enough to know the racial breakdowns on subtests. My recollection is that African-Americans were closer to average on verbal (the supposedly culture-loaded sections) but worse on math sections. Still, the WAIS is paper-and-pencil, still symbol driven.