I'm not going to get into an argument on what constitutes a game or sport. My vote is motor racing, particularly F1, Nascar, Indy etc. You have to have an innate talent first, then loads of practice and training. You must be physically fit because you have maintain a level of consistency and concentration for hours on end. The same could be also said of air racing, perhaps more so because it's in three dimensions.
On the other hand, I would consider soccer very skilled. A nephew of mine is a very talented footballer, already on the Ireland junior soccer team and being actively scouted for several big name clubs in England. He's talented to be sure but the amount of work he puts in for it is amazing and when you watch him in action you can see the extraordinary skill he has developed. In the future I'm particularly looking forward to visiting his huge house and trying out his Ferraris and Aston Martins.

Golf is also a skilled game in my opinion. Because no two days are alike, no two golf courses are alike. Golfers have to adapt continuously. That takes skill. I'm not a golfer but when I have I showed some small talent. But it is really difficult even if you're talented and well practiced.
But at risk of never being allowed set foot in America again, I don't rate US football or Baseball very highly.

For the same reason, Rugby and Cricket are wouldn't be high on my list either. So there goes any chance of visiting Britain soon.
But lest I be considered biased and at the risk of being burned out of my home and deported. I reserve my greatest disdain for those two peculiarly Irish 'sports' of Gaelic Football and Hurling. If there are more skillless games, I haven't seen them. Hurling involves thirty men with sticks fighting over a tiny leather ball, spectators can hardly see, with lots of running and often random looking scoring. Gaelic football is not much better the same thirty thugs but without the sticks and a bigger ball. You can handle the ball and run with it but you can't just throw it into the goal mouth. No you have to punch it in or kick it in. So the biggest skill of all is to learn how to make it appear you're punching the ball while actually throwing it into the net. If there's one benefit of those games it keeps the big apes who play it off the streets. If they weren't playing these games they would probably spend their time battling neighbouring towns and counties on the roads with knives and pick axe handles.

Just as well this this forum is anonymous, otherwise a mob would be forming outside right now!