Therefore, it can't possibly affect your chances to win like it does in dice. It is 50/50 in terms of winning or losing for two players before the cards have been dealt (if we discard the ramifications of skill and expertise from the equation)
A house edge does not only mean a certain amount of advantage of the casino over the player in terms of winning chance. In a dice game, your winning chance could also be set at 50%, which means the dice site does not have any amount of edge over you in winning probability. That means that "It is 50/50 in terms of winning or losing" just the same. But the house edge is in the payout or winning prize. Your chance of winning against the house may be 50:50 but your winning prize will not be x2. That means the house still has the edge over you.
In a poker game, you are playing against another player but a portion of the winning will go to the house. In which case, the house wins every time a game ends, regardless of who wins. This is also the same rule that applies over sports betting. That may not be aptly called house edge but it is somehow similar to that.
I understand the point of those that think the terminology is useless as long as you are losing some of the money but the terminology matters, in the case of the sports bets that is a house edge as well because you are not betting against other players but against the house and they give themselves an advantage no matter which line you decide to take.
But in poker they just take a fee if you are playing a tournament or they take a small percentage of each pot if you are playing for cash, the fee is there because they are providing you with the platform to meet other players and that is not free, obviously they are profiting from this but it is not a house edge, this is more similar to the fees an exchange charges for their service.
How to distinguish the two? If the house wants you to lose and they want to win then you are facing a house edge, but if the house does not care about whether you win or lose then they are just charging you a fee.