I will try and give you some idea as to why poker is different from other gambling activities.
The biggest problem with trying to explain why poker is a game of skill to a non-poker player is that in order for them to understand that that its a game of skill, you have to explain how to win at poker, and this is difficult to do because its a game that takes so long to learn, its impossible to sum it up into a single 1 hr lecture.
However, Dusty Schmit, in his book came up with a really neat way of showing the presence of skill. Rather than talking about winning, he turns the situation around and talks about losing!
If I put a gun to your head and told you that you must lose the next hand of poker, could you do it? Even if you held AA could you find a way to lose?... I think you could.. you might make a bad fold or something, but you could find a way.
What about a game like roulette? Could you find a way to lose there? Are you as a player able to influence the times that you lose? In this case no, you cannot do anything to make yourself more likely to lose than the odds dictate.
So when playing a game that you cannot increase the chances of losing you are purely gambling, but when playing a game where you can increase the chances of losing, you are playing a game of skill.
Then consider the flip side, if you can increase the chances of losing, you can also increase the chances of winning.