Yeah, Vvardenfell is pretty much a volcano in itself, the Red Mountain being only the tip of it. Actually, the Red Mountain was initially called Vvardenfell, then the whole island took the name [big assumption]when Vivec exasperated Vvardenfell from Mainland Morrowind (I'm not sure about that, I can't remember where I read that Vivec separated both lands)[/big assumption]. And if you look at the Molag Amur region, it has lava pools and rivers. I suppose this is actually as if you would cut your skin down to your veins, it may very well be magma from inside the supervolcano. And if you look where the region is located on the map, it's pretty close to one of the shores. Though since the Red Mountain has already erupted once before that, I'm quite surprised the whole island isn't ashlands or region like Molag Amur and it actually formed the foyadas. Maybe it's just because it was not totally "full".
The reason for this are retcons in the Morrowind game. Originally, the game Morrowind was supposed to contain the whole province of Morrowind (see http://www.imperial-library.info/maps/concept_morrowind.jpg), but this proved to be too ambitious. Up to then, Vvardenfell the island and Red Mountain were one and the same. You can see Red Mountain from the city Firewatch on the eastern mainland (see http://images.uesp.net//b/be/AR_Place_Fort_Firewatch.jpg). Then the rest of Morrowind was cut, but the island still looked very fiery with the foyadas being streams of lava (see http://www.imperial-library.info/maps/vvardenfell_map.jpg). I guess the devs found this to be too boring, so they moved cities and environments over from the mainland to the island.
This won't answer the question whether all of Vvardenfell represents the volcano, but I still like to think so and attribute the relatively flat appearance in the game to game engine limitations.