Why it works
Black has done the hard part: accepted both Danish pawns, traded a pair of knights and even swapped the dark-squared bishops into White's b2-bishop. It feels like time to tidy up — and 10...O-O?? tidies the king straight into the crossfire. 11.Qg4! creates an unanswerable double grip on g7: queen from g4 and bishop from c3 both hit the one square only the king defends. The engine score after castling is not 'worse' — it is a collapse (+17 within a few moves in the line). Black was already under pressure; castling was the one move that lost instantly.
Refutation
The only fight was 10...Qg5!, offering the queen trade that kills the g7-battery before it exists. White is still clearly better after 11.Qxg5 — the two open files and the monster on c3 are worth more than Black's extra pawns — but there is no forced disaster. In the Danish accepted, Black's king often has no safe address at all; that is the gambit's real price.