[supernewton]

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!

[zahlman]

I've seen people teach by playing the open-face (or otherwise simplified version) of a single turn as a way to give an overview of core mechanics.

Naturally, this works better if the 2 hour game consists of dozens of 5 minute turns rather than a few half-hour ones.

If you show one hand of Texas Hold'em, and don't actually play it, but instead talk through what players might be thinking at various points, then you not only cover the mechanics, but sell the game (through the rhetorical device of dramatic irony: you emphasize that the players don't have complete information, and may try to mislead each other, and may come to wrong conclusions even without such deceit, and of course nobody knows what will come on the river...). But of course, it's difficult to disentangle that from a strategy discussion.