Alienware X51 R2

As far as dimensions go, you should be ok as I believe the x51 can accomodate fullsized cards.

PSU-wise, I don't honestly know - but IIRC there's an external power brick that can be changed.

That being said, you should have a reference card (to blow the air out of the vents) like the MSI GTX 960 one you linked, rather than the dual-fan situation like the 660 given the compact nature of the case - you'd have additional heat not originally budgeted for in the chassis design.