So I've done four matches online (lost the first two, namely because I was kind of clueless, then one the second two, against the same guy). I think it has a lot of potential. Two negative points though:
-You can in fact use amiibo online. This means there are four characters (perhaps a 5th or 6th of the roster) that is locked away behind some very expensive and inaccessible "physical DLC". I fought against a Marth and a Ike on one team. Not sure what this will mean in the long run (balance), but it's not a good thing, at best.
-It's pretty much required to do the campaign first. Your reward for winning (and coins per kill) is paltry compared to what doing missions will get you and you still won't have characters to play with. This isn't that big of a problem, but it means that the multiplayer is primarily a post-game activity, or at the very least, only really desirable a few missions in. Doing multiplayer does get you coins for campaign use, which may be a good or bad thing depending how you look at it.
Anyway, there's a decent number of maps to play on (I've only played on the first one, so far). The limited perspective really shines in this mode I think, the whole TPS style really starts to make sense. Aside from having a lot of fun with it, I can't make any conclusive statements on it (and have become a little tired of typing lol). I could see myself getting really addicted to it. I think finding matches will be tough in the future though. I also have a feeling there will become really overpowered shit in the game, it seems pretty unavoidable (hopefully its fun overpowered shit).
Actually, reading the words from Nintendo carefully, it seems there is no specific weapon. It simply carries over your medals which in turn unlock weapons. They are simply saying that any weapons unlocked (due to medal count) will be unlocked in the retail game.
Anyone with different first-hand experience is free to correct me.
I'm fairly certain Phoenix Rifle is the exclusive demo reward. Its placement in the sub-weapon list (at the very end) certainly makes it look like it. It's not a very useful weapon, especially compared to Tom's unique one (although I did use it against the explosive enemies until I got him).