Seems like you could the same by just holding your breath and putting yourself in oxygen debt?. We used to do "hypoxic breathing" in swimming, where you only breath after a certain # of strokes during freestyle sprint work.
Or just take some epo boost and increase your red blood cells.
Ali, essentially yes, it will play with partial pressures by increasing ventilatory dead space (P-02 decreases as it would with altitude gain), as well as increasing the work of breathing, and the work of the heart. This will influence cardiovascular function and the hemoglobin curve through a few pathways depending on time. However, P-CO2 and relative humidity increases, and even with the exhale valve, it looks like there's also re-breathing CO2 which is typically not a good idea when your body is in a high demand from work.
Whether it's beneficial or not for an individual in question, a physician needs to look at the overall picture.
There's a WHOLE lot more to climbing (or doing anything at altitude) at altitude than just being harder to breath due to less O2 available and in your lungs. Buff hit on a few of them. The partial pressures in all your tissues, (whole body, not just lungs) are affected due to the elevation. I suppose these masks might possibly have some positive side effects, but they don't do anything systemically to prepare you for altitude work. The fight training actually makes a bit of sense. Getting blasted in the nose takes away much of that breathing path. Then you have a mouth guard taking up much of that space. Then, you have your teeth closed around that mouth guard so your jaw doesn't get broken the next time it gets hit... Not much flow path. That's where Wanderlei's trainers came up with the snorkel and tape idea.
I would imagine the Bas Rutten thing or the snorkel and tape would work for a fighter because it still makes them keep their jaw clenched...
Anyway, this is a climbing forum, sorry for the derail. I think the mask is ridiculous for climbers training for altitude.