"Game of skill" and "game of chance" are not disjoint sets: they overlap at poker, backgammon, bridge, and many others. Any game can have a randomizing element like the deal of a card or the roll of a die, and yet still have player choices and strategies that lead skillful players to win more often than less-skilled ones. Would you call football a game of chance because they flip a coin to choose field sides at the start?
"Pure" games of chance are those where the player makes no choices after betting: baccarat, roulette, craps, and such have only one player choice: bet or don't bet, and the outcome of the bet is based wholly on chance.
Poker is not like that. You see cards first, and then you base you decisions to bet, fold, or raise based on the cards, your position, your stacks, you opponents, and other information. Which player will have the best hand is determined by chance--but which players will stay for showdown, which will leave early, which will win the pot, and how large the pot will be, and how those results will add up over time, are heavily influenced by player choices.
It is possible to make bad choices and still win, for a while, just as it is possible to make all the right choices and lose. That's why bad players keep playing. But over the long run--and that generally means months, years, thousands of hands--those who make better choices will win the money of those who make poor choices.
Of course the best choice is to be the house. :-)