Indirectly. The actual spike of pressure that ejects the magma comes from the gasses dissolved therein. When the magma moves up, the pressure drops and the gasses become oversaturated and thus prone to violent release.
The gas bubbles result form when pressure is reduced, like you mention. So there's actually less pressure near the surface, it's just more erratically applied. The pressure of the earth's subsurface is proving the animating force.
Indeed. I just wish we could get a better sense of the scale, which is always hard in nature shots devoid of trees or human structures. A productive use of AI would be to place some houses and automobiles in the video for scale.