You don't need much pressure. Professional players use circular breathing, so their cheeks need to puff out. Or in the case of Suren Asaduryan, balloon like bullfrogs. It's also common for a solo player to be accompanied by one or two others playing a drone or a very slow-moving pedal ("dem duduk") - the accompanists will circular-breathe too.

Leeneia's link shows a common problem with this stuff. The uploader is a nutcase Armenian nationalist bigot with a huge axe to grind. You don't need to swallow that crap to listen to the music - there are other sources, albeit almost all YouTube videos allowing comments degenerate into a frenzy of multilingual obscenities in three or four character sets. The same music is played by musicians from Armenia, Turkey, Georgia and Azerbaijan: they frequently collaborate with each other, and I don't know of ANY of them who subscribes to the sort of madness many of their fans go in for.