Using Atari's image I added a green line showing signal flow using the three valid closed switches. Since the outhole switch triggers the tilt in this scenario we'll start the signal path on ST0. The signal passes through the outhole diode in the correct direction, through the closed outhole switch and appears on I7 where the MPU can read it as a valid switch closure. This is normal.
The signal also passes through any other closed switches on I7. It's the job of the diodes on each of the other switches to stop the signal right there and keep it from going the wrong way through the switch matrix.
However, the shorted diode on DT #1 allows the signal to flow the wrong way through the diode instead of blocking it. The signal hops on ST2 (vertical line) where it can pass through closed switch DT #2 and appear on I6.
The purple line shows the signal flow as interpreted by the MPU. It knows nothing of the shorted diode. It only knows the signal started on ST0 and can be seen on I6, and the only way it could have gotten there is through the tilt switch. So it tilts the game.
Xenon switch matrix (resized).png