Imagine entering a tennis tournament. Each player pays $100, and the top 10% of all the entrants are going to get paid some money. They higher up the tournament you get, the more money you will win, with the winner of this tennis tournament getting the largest prize.
What would you call the people that were trying their best to win the tournament? Would you call them "greedy"? Personally, I wouldn't. As others said, I don't think that would be an accurate use of that word.
Just my opinion, but I don't see poker as any different. Tennis is a game of skill, and the more skillful players are going to win the majority of the time, but not always. Poker is a game of skill, too. Yes, it has a great element of luck, but in the long term, the most skillful players will win the most money. In that aspect, it is fair.
CAN their be greed ANYWHERE in either of these examples? Of course.
Tennis tournament with greed: One player clearly outclasses all the others. Nobody can possibly beat him. He enters the tournament, and wins. The tournament is a local tournament for the townspeople, and although he makes money playing tennis professionally, since he lives in town, the rules say he is still eligible to play. So time after time after time, he signs up for the tournament, and always takes the top prize money.
That's greed. Poker has many examples of people being greedy, too. Sometimes being greedy in poker ends up costing you to lose money. Someone gets on a big lucky streak and because of their greedy, they don't know when to stop playing once they start losing. Their greed causes them to lose all their money.
With all that said, I wouldn't label poker as a "greed" game, for the same reason that I wouldn't label a tennis tournament as such.