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What are the rules of castling in chess, and why is there castling in chess 960!?

I somewhat remeber reading that this format is about playing against book opening, and I thought there is no castling.

Magnus does a castling from king d1 rook h1 which I didn't even know its an allowed move! https://lichess.org/broadcast/fide-freestyle-chess-world-cha...

After castling, the final positions of king and rook are the same as in classical chess. Castling prerequisites are the same as in classical chess.

source : https://en.wikipedia.org/wiki/Chess960#Castling_rules

When I clicked one of the game, the initial position is wrong. I clicked another game and it was wrong as well. Am i wrong?

Indeed. This is Chess 960.

>Chess960, also known as Fischer Random Chess, is a chess variant that randomizes the starting position of the pieces on the back rank to eliminate memorized opening theory and emphasize creativity from move one.

This is great, thank you for sharing.