It isn't that debilitating, it just affects how
precisely you can judge distance. With very fast projectiles, there's no advantage to speak of, and sometimes disadvantage in having both eyes open (if you're aiming down the sights of a gun, for example, you can only use one eye, and the other eye will just interfere). For slower projectiles, like thrown objects, or extreme ranges, like artillery or catapults, accurately judging distance is important to getting the right parabolic trajectory. But for throwing, the effect is probably negligible for just having only one eye, and unless you're going for a moving target and need to judge your lead, it's certainly not going to affect whether you miss to the left or right.
For a practical example, consider FPS games. Can you judge distance in them? Easily. It's no harder to aim guns in them just because there's only one "eye" in the game, it's really not very difficult for players to judge distances and throw grenades and other parabolic projectiles with a lot of accuracy. They do have to re-learn their throwing ability, but you don't get "Oh, I misjudged how far that was, darn my lack of depth perception" a lot, it's usually misjudging what angle to throw at to get the distance they're going for, which is a function of player skill, not an inability of the display to show distances clearly.
I've played those same shooters on a full 3D monitor, and I can tell you, it really isn't much of a tactical advantage. Everything in the game, everything you need to know to fight accurately, is perfectly clear in 2D -- 3D is just prettier and more immersive. There are advantages to that kind of depth perception, but the practical implications are actually not very big.