Yes, I have shot rifles with the Aimpoint Comp, several of the long tub Bushnells, the short and wide Tascos, C-More, Eothech, Trijicon the Bushnell micro, Burris Speed Dot, Burris Fastfire, and Bushnell Micro.
Can you ethically shoot game at 200 yards? Yes. The sights are capable. Some have very large dots, which are too large for 200 yards. The Aimpoint comes in fixed sizes, 2 MOA or 4 MOA. The 2 MOA is definitely small enough to shoot clay pigeons offhand and very quickly. Even when the dot is wider than the target, you can hit it, such as a shotgun shell standing up, and shooting it with a 3 MOA dot.
The Fastfire and the micros are small enough to mount on a handgun. The micros by Burris, Bushnell and Aimpoint lock onto one rail slot. The Fastfire, and similar ones by Doctor and Zeiss, will also fit into a notch made for them, such as on the FNP pistol. The Aimpoint Comp will mount on one rail slot, but covers 3 of them. It will mount non a single Warne or Leupold scope base, using a very wide ring. So will the Burris Speed Dot.
The Aimpoint has phenomenal battery life, like a year. The Trijicons use no battery, gathering ambient light into fiber optics and channeiling it to the dots.
If you have never shot one, you should buy an inexpensive one and try it before spending $400 or more on an Aimpoint, Eotech, Zeiss, etc. These Bushnells and Tascos are far better than you might think. The long tube 1-inch and 30mm Bushnells come with adjustable levels of brightness, several sizes of dots, crosshairs, and different colors, so they are excellent for finding out what type of reticle you want, dot size, color, and size of tube.
A major factor will be mounting on your rifle. A long tube Bushnell or Aimpoint 9000L will mount on a magnum action in QD rings. The Aimpoint will have larger occullar lens, but you need to see if your bolt handle and hand will clear it. You don't want to jam your fingers while trying to load a second shot which you really, really need. So the make and model of your rifle, the mounting system, and any other scope you will be using in conjunction with the dot sight and the iron sights is a factor which will limit your choices.
One more point: You cannot just compare MOA to MOA, because of how the sights are mounted and used. 2 MOA in a sight on a rifle close to your eye is going to be good for shooting out to 200 yards. But on a handgun, 24 or 28 inches from your both eyes, you might want 5 MOA or 8 MOA. Again, this is why buying something like a Bushnell or Tasco with a lot of adjustment options for around $100 is a great way to learn what you need for your intended application.