The answer is, of course, Shohei Ohtani.
I’ll go with the ‘all around’ in both men’s and women’s gymnastics, or the decathlon.
Whack-a-Mole is a difficult sport. You never know where or when the next one will arise.
You get to stand still while hitting a baseball. There are lots of sports that require the player to interact with a fast moving ball or other device while the player is also moving. Hockey (ice and field), soccer, rugby, lacrosse, American football, etc.
And basketball! 
Another way of asking the OP’s question is,
Who is more coordinated than Michael Jordan? I wouldn’t say that Michael Schumacher or Ayrton Senna or Lewis Hamilton is more coordinated than Michael Jordan. No way they are.
Or…
Who is more coordinated than X? (and fill in your X)
I see no good reason for putting him as the standard by which others are judged.
What elevates basketball as a co-ordinated athletic endeavour over and above say football or tennis?
Hockey, IMO. The ice surface puts the players on top of the “insanely well-coordinated” list.
There are a few differences between hitting a baseball and interacting with those other balls/pucks.
- Baseballs are thrown with a deliberately unknown speed and trajectory in order to fool the batter.
- Other balls/pucks, when delivered by a teammate, are intended to be easy for the receiver to interact with.
- When other balls/pucks are delivered by an opponent, the goal of interaction is to primarily disrupt the path of travel, not redirect it with a specified intent.
- Baseballs must be interacted with while traveling at a relative speed of nearly 100 miles per hour, and must be hit with a stick being moved at 70 miles per hour the opposite direction.
At the highest levels, participants in many sports need exceptional coordination. I think it’s more interesting to think about what sports need the most coordination for basic participation.
I think the most precise coordination of limbs is required for basic participation in golf. If you don’t hit the threshold of being able to swing a club and hit the ball straight-ish and with some distance, the game is a painful slog, objectively awful. Forget about competing, you can’t even play for fun.
Playing fast pitch baseball when you can’t hit sucks, but you just take your 3 swings and go back to the bench, you’re not spending 5 hours in a pathetic death march chasing down squibs and worm burners all day.
Because I played football (my favorite sport; I was a decent QB in my day), basketball, and tennis. Baseball – I played 3B, and some SS. And golf. And racquetball and table tennis. And badminton. I’ve done a little car racing, too. And some motorcycling. And parachuting and rappeling. And soccer. And whack-a-mole too, yes. I’ve gone curling. When I was on the track team it was javelin, shot put, and the hammer. I’ve played lots of darts. Shot a lot of pool.
Decathlon - yes, some coordination is required for those events. And the gold medal winner is usually dubbed the best athlete in the world, but that’s only because some king said that to Jim Thorpe when he won, almost a century ago.
I’m fairly decent, athletically, and have won some awards in different sports.
IMHO it is basketball in terms of overall coordination. Dribbling with both hand, behind the back and through the legs. Moving quickly while being aware of all 9 other players on the floor. Going up strong for a shot, or playing a bang-bang low post challenge, having a soft touch with your jump shot.
Other sports requiring lots of coordination:
ice hockey - I never played but I can appreciate players’ coordination there
gymnastics - I never did this but yeah, the rings, the high bar (whatever it’s called), the horse, floor routines, … yes, lots of coordination there
So yes, ice hockey and gymnastics require a lot of coordination. More than the decathlon.
But IME, it’s basketball hands down.
I’ve played an equivalent range of sports to you to a good standard in many cases and basketball wouldn’t even have figured in my top ten.
Okay, that’s fine. Then what’s your vote?
probably ice hockey
Yes ice hockey is way up there. I can go with that too.
Extremely few people in this world can ever start on the exclusively expensive path of becoming an F1 driver, and there are just as many = few F1 drivers as there are slots for them, so the number of F1 drivers is irrelevant to the question at hand.
There is probably a relationship between height and nerve conduction speed. Most gymnasts are not huge. Basketball players are well coordinated but many of the tall ganglies in our high school gym class were not. Apart from basketball, I don’t see players being more coordinated for daily activities than more compact athletes. Hmm… what day-to-day activities require a lot of dexterity?
IMHO, one way to measure the “requires the most coordination” is if you could reasonably teach it to your average high school gym class and by the end of the semester have all of them be able to perform the sport amongst their peers resembling what the sport is supposed to look like.
I don’t think you could reasonably do that with something like ice hockey or auto racing.
I will also chime in with ice hockey. It requires a high degree of coordination in order to shoot, pass, or handle the puck effectively if there is no one else present, and even more coordination to prevent a steal. You have to be able to move both backwards and forwards and stop on a dime - at the professional level you have to be able to do that at 40 km an hour (25 mph). You have to be able to react quickly to other players, either to deliver or receive a body check without injury, or to protect the puck. And you have to do all of that at the same time, while viewing the ice and positioning of the other players.
Hockey players also routinely take a “pass” - six ounces of hard rubber moving at 100 mph - and manage to hit it with their 1”-3” wide stick to redirect it into the goal.