On the other hand, when you are playing against other folks (as in poker), the house edge becomes kinda irrelevant because it is the same for all other players as well, but you win not by taking the casino's money but the money of other players. And that's the true beauty of it
I haven't ever played poker. But I think when you play poker, there is still some profit go to house.
For example if a user lose 100$, you won't win 100$, you will win lower than that as 1$ (for example) goes to house.
I wouldn't call that a house edge
Edge means an advantage, in this case the advantage of the casino before the player. But since casino is not playing in poker (unless you are playing against the house, of course, and not the other human players), you can't consider this percentage taken from your winnings a house edge even if it does go to the house. I would suggest to think of it as a fee, a playing fee of sorts. Most importantly, it doesn't take anything from the advantage you may (or may not) have over the other players