PUZZLE in TWO: "Two Squares move by W. King"
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I would have never figured yours out. I was thinking 1. Bb2 ... 2. Re2, but the queen messes things up. Fun puzzle.
The fact that the king is on e1 and rook on h1 should be a clear hint to experience puzzle solvers 
Suppose it were black's turn. If he moves his queen anywhere but d4 and f6, white mates by giving a discovered mate with the rook on c2. If he plays Qd4, then Qxd4 is mate. If he plays Qxf6 however, there is no mate.
Other black moves are 1... d5 and 1... f4 when white also doesn't have a mate in one.
So it makes sense to let the only piece that doesn't play a part in any of the mate, get involved and threaten mate. 1. O-O! still has the same mates if the queen moves somewhere other than f6, and if 1... Qxf6, 1... d5 or 1... f4 then 2. Rd1 mates.
good analyzation Phobetor, only one of possible checkmate by white I see in your solution.
If someone can see some other moves just list it, moves for checkmate by white in different positions. 2.Rd1# is solved by Phobetor.
Two moves mate.
There are lot of possible moves by black, but still checkmate in two. Can you list down some moves in two. No peeping on movelist.