Chess Game #2

Why on earth would white play a move like Rhe1?:)
White is much better in the given position simply because black has seriously weakened his king position, and white is free to castle on the other side, where he's not weak, and black has not even started a preparation for a counterattack.
(If long castling is not legal here for white because the king has moved, the king would still be safe on e2. White would be better, but the position is a bit more complex).
I'll asume o-o-o is legal for white.
White is ready with h4, 0-0-0, rdg1 (after castling) and other easy to find setup moves. Black has no corresponding play against white's position.
After short consideration, I'd play 1.h4 as white. Open lines immediately.
Black has to play 1...Bxg4, because
a) If he plays gxh4, after 2.Rxh4, followed by g5 to either get the knight there (after exchanges), or open up the position in front of the black king a bit more, then 0-0-0 and bringing the other rook... Black is dead there.
b) Anything else (other than Bxg4 abd gxh4) allows black to get an open h file for free (and there is the immediate threat of hxg5 hxg5 Bh7+ Kh8 Nxg5, which is the end for black, so black doesn't have that many options too). For exampe:
1...f6 (to deal with the aforementioned threat) 2.hxg5 fxg5 3.Nxg5! and black can't take the knight
so, 1.h4 Bxg4 2.Nh2
White has time to create a decent attack because black has no counterplay at all.
2...Bh5 (the bishop is needed on g6 for defense). 3.hxg5 hxg5 4.f3! (castling long has to be achieved... Unfortunately, it is illegal to castle through check, remove black's contorl of d1! white can play a bit slowly here, because, as mentioned before, black has no counterplay).
There would follow Qg2, 0-0-0, Rdg1, Ng4..... Black is in a dire situation (maybe already lost).
OK this is another game from home, please analiyze it and tell me who's better...