Nice article, agree the main difference is the lack of perfect information in poker. Everything you do in chess is through skill and there is no chance involved. It would be interesting to have another article comparing poker to (contract) bridge. I used to play bridge and it is also a game of incomplete information and the rubber format like poker can be used to gamble. Main difference is that bridge is a cooperative game where pairs help each other to win the hand by trying to share information through the bidding and defence of play of the hand. The element of chance in Poker is eliminated through the volume of hands played. In tournament bridge it is eliminated through duplication where each pair competing play the same hands. One similarity of these games and also games like Go is that they may appear relatively simple once you know the basic rules but are in fact incredibly complex and nuanced in their play - See more at: http://www.pokerstrategy.com/news/world-of-poker/How-similar-are-chess-and-poker-_88829/#sthash.gdxz68VL.dpuf
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Nice post.
I tried bridge years ago, and like you say the basics are simple, but to play with any skill was beyond me. Of course, I didn't stick with it for long, maybe if I had I'd be playing with Bill Gates now... 
You could probably also include backgammon. Another strategy game where in this case the doubling cube adds to the gambling element.
There are also quite a few pro poker players who came from backgammon origins.