Who's giving away the reward bitcoins? If it's literally mining, then a game won't help at all at mining, since nowadays all mining is done with ASICs. It it's given by a third party, like a company, then what does this company win by giving away free bitcoins for people playing their game? It could work if it was ad-driven, but I don't think this would catch at all.
Also, why “gorgeous graphics”? The Minecraft graphics were made that way on purpose, because it looks cool to some. Is there any reason why gorgeous graphics are needed for this?
It would be an abstraction. Gamers would have to be miners too. Of course no one would be giving away free Bitcoins, but that doesn't mean you can't use Bitcoins in-game. I suppose, if we wanted non-miners to get involved with Bitcoin, then yes, miners or other Bitcoin owners would have to create an incentive to play this game by providing their Bitcoins. For example, hide and seek scavenger hunt with Bitcoins at virtual 3D positions in the virtual world.
I think it needs gorgeous graphics for offline gaming. But mainly it's because we don't want it looking like Minecraft. It'd be more of a marketing thing.
