Hmmm.... I can imagine how to translate Dominons into RTS and RPG (maybe even MMORPG or a city-builder), but FPS seems a bit stratching it. There is little, if any, shooting. Maybe a Zelda-esque thing...
I personally would enjoy a steampunk dominions (I love Dominions fantasy, I would like to see what Kristoffer does with modern stuff). Space game: Mayyybe, but those focus more on technology and space ship design normally, which isn't very Dominionsey (though they could suprise us...
).
As for what type of game, I don't particularly like RPG's (just a personal opinion, ignore me). I think a Dominion's RTS could be fun, though a good deal of the original game would probably change in the translation.
I will end with something very hard to do: make a Dominions Racing Game!