I think it would be better to qualify it and say that the house always wins in the long term. And that's just taking into account the house vs the player. If we take into account other factors, the house can also lose, such as when it fails to attract enough players and due to its operating expenses it goes bankrupt and closes.
I don't know why I am even replying but I felt people must know what's wrong with this mentality - The House Always Wins
Look, gambling is meant for entertainment. Do we ever say the circus owner always wins or the owner of the live event always wins? No. That is because we consider going to a live event by purchasing a ticket, as entertainment. The mentality of earning from gambling is what makes us say "the house always wins". The house always wins because we are losing more than we should have lost.
Consider gambling just as a means of entertainment and you will never have problems.
That's what I tell people but it's not essentially different from the circus in that in the circus you don't expect to make money. The ones who get carried away with emotions trying to make money are the ones who end up in trouble.