It's not, really. As Galton discovered, reaction time correlates with other kinds of intelligence.
I've read that modern tests show that some groups have a faster physical reaction speed, but a slower mental reaction speed -- e.g. the signal gets from eye to brain to hand slowly, but the hand moves fast.
The thing about football quickness and reaction time, is that it is nearly all physical reaction speed. You rarely think at all. You've just repeated in practice what you need to do so many times that once you're on the field it becomes automatic. Running backs and receivers for the most part just need to be able to get downfield really, really fast. The offensive line needs to memorize more plays and formations, so a few points higher on the Wonderlic might help them in that regard. But once you're on the field, you aren't "thinking" in the sense that most people use the term. I don't think the Wonderlic scores even figure very highly into what makes a great football player. If anything, the scores are used by the coaches and trainers as a metric for figuring out the best approaches to teach the players what to do.
note: I played tight end throughout high school. I'm a bit distraught that this infographic suggests that the offensive tackles might have been smarter than me.
I don't mean mental reaction time in the sense of quickly weighing possible courses of action -- I mean literally the time it takes for you to register a change. The simple reaction-time experiment is to hold a ruler in front of someone, so it hangs down; they have a hand wrapped around (but not touching) the end of the ruler. You let go, they grab it, you measure how far it fell to see how fast they reacted.
The thing is, some people will start to grab it fast (high mental reaction time) and other people will actually touch it sooner (slow mental reaction time, faster physical reaction time). If you're running in a zig-zag pattern, this would mean that you would start turning faster, though other people might be able to execute a complete turn (start to finish) faster despite lower IQ.
And I would guess that the larger the muscles involved, the more important physical reaction is. So if you're talking about moving your fingers (as in the ruler example), then mental reaction is going to be more important, but if you're moving your whole arm or your legs, the physical reaction is more important.
I've read that modern tests show that some groups have a faster physical reaction speed, but a slower mental reaction speed -- e.g. the signal gets from eye to brain to hand slowly, but the hand moves fast.