This is covered by the article. A board game might take 4 people and 2 hours to play. If your three friends didn't have fun with a board game the first time, they probably won't want to play again, and so you won't be able to play again either. Therefore there is a strong drive among boardgamers to play the "full" game the first time, because there might not be a second time.
It also adds extra difficulty to design a game that even has a simple version that is fun to play. Take your Texas Hold'em example, imagine it takes 2 hours to play one game. If you start with a version that has all cards face-up and no betting, people would conclude that Texas Hold'em is a supremely boring game, and wouldn't bother to try the full Texas Hold'em experience!
It also adds extra difficulty to design a game that even has a simple version that is fun to play. Take your Texas Hold'em example, imagine it takes 2 hours to play one game. If you start with a version that has all cards face-up and no betting, people would conclude that Texas Hold'em is a supremely boring game, and wouldn't bother to try the full Texas Hold'em experience!