The vine is probably attached to one of those hovering warships the Martians fight their battles with. They sort of resemble those big hovercraft that cross the English Channel, but they can hover at much higher altitudes. The Martians (or better said, the citizens of Barsoom) prefer to fight at high altitude for some reason....maybe because it's cooler up there....maybe because it allows for the fighters to fall screaming to their deaths far below, which is much better from a dramatic perspective than just directly falling a few the ground in the usual manner.