Well yea, profiting from the mistakes of others isn't luck. You control your own moves, so how you move them of course that qualifies as skill. In an extreme example, you may get lucky that a player intentionally moves his units out and away from his centers; it is still your "skill" that allows you to take advantage of it and walk your units into them.
The mistakes others make aren't always luck, either. Sometimes you use your skill to induce those players into making those mistakes. In fact, that's often (always?) your goal. However, there certainly is a factor of luck in games. It is luck, not skill, that you draw opponents that do not realize that hey, maybe they should try and stop the guy who is going to win instead of continuing to fight amongst each other. It's luck to get an Italy who doesn't realize or care that France only needs a couple centers to win and decides to vacate Naples, Rome, and Venice and move east.
I was simply addressing the fact that luck certainly does exist in this game. They are also often intertwined, as well.