Donald Trump is the leader of the largest government and military in history of the world. When he says "I like a company should X", it has more pull then a private citizen. When the NFL began taking $$ and favors from that government, they now are in business with the government, and when the leader of that organization says something, they can only stand up to him so much.

Now, if they were purely private, then his comments would have not power behind them. As you said, he didn't enact an Executive Order. He threatened their tax exempt status and they caved.

Maybe if the military didn't pay the NFL to have the players on the field during the Anthem, this wouldn't be an issue. But they do.

It's funny to me how the fans want the players to stand for the Anthem and "don't want politics in football". Bringing the military and nationalism into the football is political. Fans can't have it both ways. They are freaking out over something that wasn't part of the game less than a decade ago.