High altitude walking and climbing is a red herring. That is achieved by acclimatisation over weeks. Anything less results in altitude sickness, incapacitation, unconciousness and death.
The video shows a small increase in blood oxygen levels by a very laboured breathing technique that seems not too dissimilar to hyperventilation. I don't really think that is a viable or safe way to operate an aircraft above the usual oxygen limits. I wouldn't fancy keeping up that technique for 5 minutes sitting in a chair at ground level, let alone an hour, piloting an aircraft at high altitude.
In answer to the point in your first post, this is not pressure breathing as the RAF would know it.