You have absolutely accurately established what defines the game as "gambling" - it is the influence of luck. It is the factor that allows any beginner to hope that he can win with the first bet in the casino, or in the first match in poker. How many times have I seen the showdown, and when the professionals with a high probability of winning this probability did not work. It turns out that this hope for a wild win attracts people both to the casino and to poker. After all, as we know - beginners are lucky, and it turns out that for them luck is an ally of the game. And when they get a win, they think that it is forever.
Unfortunately for those newbie players even if they can beat a professional once or twice, they have no way to do this consistently and the professional will recover all the money they lost if they keep playing, since poker despite being a gambling game, it is also a game of skill, so it is very common for a newbie gambler to get overconfident about their win and think they can beat anyone, only to find out later they were wrong on their assessment and suffer terrible losses because of it.