I don't think this is accurately said, it is right to say that the casinos do not only make money from house edge but however you think the casino makes money in one way or the other is still connected to the house edge. You can say that the casinos make money because they use the greed of gamblers against them but you need to understand that all these is by design. Everything was programmed to put gamblers in a trap for the house edge to work against them. That's the reason why gamblers that chase profits and losses ends up losing more in the long run.
Right. Basically, we could say that the house edge is a way for the casino to actually make normal revenue, because even if 60% of the players are winning, and 40% are losing, the casino will still be making money because the 60% that is winning is also giving a share of their winnings back to the casino, while the losers are giving everything away to the casino.
This is the reason why we always say that even if a person is mostly in profit, if they continue gambling for a long time, the casino will still have an edge because of the house edge, for example, if you lose 15 bets, and win 16 bets with 2x odds, and if that equation continues, you will still not win much in the long run because the house edge will eventually eat up your profits slowly.
This is why, we need to understand that the house will always be ahead of us gamblers, not only because most of us will eventually lose against the house, but also because they have the house edge that they take from our winnings, so they are always winning, and we are always losing even if we are winning, unless we manage to win a large amount and then stop gambling, but as long as we keep gambling, the house will always outrun us in terms of making profits.