The play in the OP is an illegal dribble.
This is specifically talked about in the "Handbook".
WAAAAYY back...even before Jurrassic's appearance on the basketball scene, there was something called an air dribble. At the time, the rules only said was that a player couldn't run while holding the ball. So, some intellegent player figured they could repeatedly tap/bat the ball up into the air while running down the floor...never letting it hit the floor and never holding the ball.
The rule that is now 4-15-2 was added to prohibit this practice. While a player may still bat the ball into the air, it much touch the floor before they touch it again. To do otherwise is an illegal dribble.
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