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Strange stalemate

There is a situation I don't get here : youtu.be/kSW_G7pQjKk?t=297

I don't know how to show a game, here is what I have :
8/1p2P3/1P1k3p/2p3pP/2P3p1/6Pr/6K1/8 w KQkq -
lichess.org/editor/8/1p2P3/1P1k3p/2p3pP/2P3p1/6Pr/6K1/8_w_KQkq_-

White promotes in e8 and the guy on the video gets a stalemate. That does not happen in Lichess, where the game continues.
I seem to understand that black can force stalemate by chasing the king with the rook, and king cant' take the rook (or it is stalemate). Though, Black could miss this and do anything else, like rook h5 for example.

So why does the game in the video ends in stalemate ?

I'm just surprised that in the video, the chess program immediatly considers this as stalemate while black could still make mistakes and lose the game. I was wondering if there is a rule that I dont know about this

It wasn't a game he was playing, it was a puzzle he was trying to solve. His screen says 'incorrect', not stalemate.

When he says 'stalemate' he is not talking about that position, he is talking about how the game will finish (with correct play from black, it will be stalemate or a 50-move draw).

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