When he picks up the ball, neither of his feet are on the ground, so when his first foot comes down, that establishes his pivot foot. Then he takes 2 steps for the layup. Questionable, but not a travel by the rules.
Depends on when you are counting the steps. The rule book says two steps - one with each foot. By your first post, you said he get to put his first foot down then take two steps. E.g., if you put your left foot down you can step with your left then with your right. That is traveling as you cannot lift your pivot foot then put it back down again.You get 2 steps on a layup. You're taught that from the first time you dribble a basketball. Not sure where the confusion lies there.That's the difference between what the rule book says and what is being allowed.You get 2 steps on a layup as long as the steps are continuous into the shot.
However, the NBA admitted they are allowing an extra step from what the rule book states.