I have seen many people training while wearing these type of masks. To keep it simple, the theory behind it is that because it makes breathing more challenging it will improve one’s aerobic capacity. I know people who do long runs and workouts with these masks. I have never used one nor I would recommended. As for the person you saw boxing, I’m not sure if that is a great idea or not. And of course as long as he doesn’t get punched in the face while wearing it ;-)!
My perspective is this. Any kind of resistance applied to a movement, whether it be resistance to a movement with your body externally or resistance to your breathing will cause a feeling of greater performance once the resistance is removed. I could see this causing your body to adapt to functioning with less oxygen and thereby improving it’s abilities when greater amounts of oxygen available. On the other hand, this is not allowing growth in the bodies pathways of receiving greater amounts of oxygen. However, being that it is an elevation mask, you would think that some people might think that it will help them in higher altitudes. The problem with this though, is that the percentage of oxygen in the air at those higher altitudes is less not the overall amount of air as with the mask. Definitely more research is needed.
I’ve never seen this mask until now. I definitely see the thinking behind it but I absolutely need to see the research behind it. If you need to adapt to higher elevations, it would seem like a more convenient & cheaper alternative than re-locating to the mountains. Again, I would have to see the supporting literature to see how training with this mask actually stacks up versus training at higher elevations in regards to cardiovascular adaptations.