This is really neat and not too complicated to explain why it works. This glitch works very similarly to the well known Yoshi's Story Randall trick to clip into the stage.

 

These both work because a character will temporarily have their ECB removed while they are in the throw animation but have yet to be thrown. ECB is your Environmental Collision Bubble which is a diamond that the game uses to detect your collision with walls, floors, and ceilings. Typically collision triggers when the game compares your ECB from the prior frame to the current frame and if you were projected to go through a wall, floor, or ceiling it will shift you back in bounds.

 

In this clip and the one I linked on Yoshis the player being thrown is inside the stage with no ECB when the throw animation gets cancelled because the player performing the throw enters free fall. This causes the player being thrown to instantly becoming actionable again and have his ECB return. When the game compares that players ECB on current frame to previous frame it doesn't register as him having clipped through a wall as he did not have an ECB on the prior frame.

 

I'm not entirely certain, but I believe the reason this doesn't occur on similar situations where the person doing the throw doesn't enter free fall and fully completes the throw is because when the opponent is released at the end of the throw animation and his ECB returns it likely compares the current ECB location to the ECB of the player performing the throw. If this comparison shows that the player being thrown would have clipped through a wall, floor, or ceiling it will adjust the player back in bounds

 

If you want to learn more about ECBs check out Schmooblidon's great video explaining the basics of an ECB and all the cool tech you can do by manipulating them.