Lots of people love model airplanes, and I bet they would love to simulate dogfights. They can't fire actual projectiles, as that would be dangerous, expensive, unworkable due to the weight and actually damage planes.
It should be possible to set up a system for dogfights using light, however. One way would be to have planes mount lasers that send out a coded pulse with a bit of dispersion, and have the other planes mount receivers with diffusers to pick up light from a lot of directions. It might be better to go in reverse, the way many shooting games do -- the planes broadcast a coded pulse from some bright LED in a specific colour and the "gun" is just a narrow sight that tries to pick up these pulses. When the gun gets one, it sends it down to the coordinator on the ground, and that tells the target plane it's been hit (possibly forcing it to leave the airspace after some number of hits, or impair the flying controls, etc.)
Of course you need authenticated equipment. If people provide their own it's too easy to cheat, and one could also just make a gun that has no barrel instead of a wide one, or have one on the ground. So some honour might be required here.
It would of course be hard to do, with no cockpit view. Some larger model planes can carry small video cameras for a more realistic dogfight of that sort, but I suspect people could figure something out. The gun could have sensors for the pulses that are wider than the actual "direct hit" sensor, allowing them to tell you when you're getting close, and even showing a screen on a laptop that is not a camera view from the plane but at least a view of how close you are to the target.