Not sure if this is what you're looking for exactly, but Trails in the Sky is pretty good. It's on GOG for PC. It has one of the most detailed worlds I've ever seen in an RPG -- almost every NPC has a name and updates dialogue after every event.
Can personally confirm that it works pretty well with WINE on Linux (even got my xbox360 controller to work using xboxdrv in xpad mode, shockingly) -- just the intro movies won't play, but other than that it works great.
Yes, Trails is very good (and Second Chapter is even better) but it is nothing like any Zelda game I have ever played. More like a Final Fantasy game with turn-based, tactical battles which are separated from the overworld.
(On your specific video problem: Trails uses DirectShow to play the videos so make sure your Wine setup can play them)
To the GP: Recettear has combat like the older Zelda games (with a simplistic shop management sim tacked on. I think the Ys series also has combat somewhat like Zelda. Perhaps Diablo clones might interest you. Which bit of Zelda are you looking for?
Can personally confirm that it works pretty well with WINE on Linux (even got my xbox360 controller to work using xboxdrv in xpad mode, shockingly) -- just the intro movies won't play, but other than that it works great.