They haven't really discussed the rewards for minigames yet, but I'm sure there will be some. As for eliminating the grind; I don't think that's entirely possible. I think the game would become a Blast-n-leave game if it there wasn't any kind of grind. Honestly, anything can be described as a grind by anyone. The game is challenging? IT'S A GRIND. The game has daily quest system. IT'S A GRIND. The game has a combat system that doesn't give you 9000 things to do? BECOMES A BORING GRIND. I think we can nit pick at it all we want, but I think the real kind of grind is when no new type of content is presented every patch/expansion.
Look at WoW, how much has really been added to it after 7 years? You can joust, the new darkmoon faire (finally), seasonal events (not many MMOs go without them, so meh), and possible a FEW other to name. Other than a few things, there really isn't anything else outside of questing, dungeoneering/raiding, PvPing, and daily quests. I think when there simply isn't enough to do OUTSIDE of combat is when the game starts to feel like a grind. I like that WoW added tons of tools to their game over 7 years, that's cool, but it's not going to sate content hungry players. I don't know if this is true, but I have to give them credit where credit is due: it's gotta be hard creating new raids and what not using a modified WC3 engine. An engine designed for an RTS.
I'm glad GW2 is going to give us tons of things to do outside of combat right off the bat, and I hope ANet adds more of this kind of content in future expansions.