You’re assuming that the deer would stand still while the atlatlist wound up and threw.
Edit: An inexperienced hunder with a bow is more likely to hit a deer in a vital area than somebody with an equal amount of practice, armed with an atlatl.
The atlatl does require more practice but not an extrordinary amount for 20 yard accuracy. The release is more silent than the release of an arrow. The thrower does have to be in position that the deer does not see him wind up and throw. Many deer are taken by darts in the United States each year. After about 50 throws i found myself hitting the target pretty well, not well enough to hunt but I could see my accuracy comming up fairly fast.
Just to clarify, an atlatl would be hand thrown and, therefore, legal. What I was trying to point out was they probably disallow artificial means of propulsion like from an explosive charge, potato gun, etc.