Most computer chess games consider castling to be a king move. You click on the king and it shows an option to castle.
What do the FIDE's rules say about this though? Is castling a king move, a rook move, both, or neither?
The FIDE rules say this about castling:
This is a move of the king and either rook of the same colour along the player’s first rank, counting as a single move of the king
As a purely separate thought on the stupidity of the current rule consider the following hypothetical case: White can castle, but both the f- and h-files are open. White plays Rf1, suddenly realises he has missed a much stronger move and quickly moves his king to g1 . As the rule stands his opponent or, as happened in a recent Soviet event, the arbiter can insist on a rook move. White calmly plays the winning Rh1-h8.