Yeah, that's how you win in poker, by having more skills than others. Luck doesn't care who you are, it's distributed absolutely randomly among everyone. So, although it wouldn't be right to say that everyone has equal amount of luck, that definitely wouldn't be true, we can still say that no one can count on having more luck than others. Hence, we are all equal in this department. But we can count on having more skills. And if we are more skillful than our opponents, we have an edge over them.
It's true that luck affects all of us and should therefore not play a too big of a role in our decision making. But this implies that we are playing a lot of hands in poker regularly to get the randomness (positive and negative luck) out of our strategy. For someone who only plays maybe one night per month poker the aspect of luck is completely different. If we meet a recreational poker player who goes allin preflop with his 22 for example, only to hit another 2 on the river, we will lose a big pot. For him the win could mean everything and he might take a break for another 3 weeks from poker and enjoy his profit. Swings in our profitability are part of every poker player, and the smaller the number of played hands the more will the swings affect our bankroll. That is also why tracking software for poker hands is so important. It will show me exactly how my swings are affecting my gameplay and if my strategy is still giving me an advantage over my opponents.