In the video, the computer is at the top of the screen, in total control of the match. When you hear the weird sound effect, it means it’s time to smash the ball.
Let’s talk about controls, shall we? To serve, you have to move the directional pad up and press the button. To hit the ball normally, you just press the button without touching the pad. To smash, you have to move the pad up and press the button. To cut the ball (slow it down), you have to move the pad down and press the button. Remember to press the button (and directional pad) early otherwise you will miss the ball. When drifting near the corner of the table, it is a good idea to change direction (going from right-hand to back-hand or vice-versa) with the left-right directional pad, otherwise the ball you hit is gonna miss the table.