The rules are a bit complex. The word "let" is mentioned 39 times in the online US Squash Rules. Under rule 12, Interference, here are some of the more common uses of "Let", "No Let" and "Stroke":
- The player is entitled to a let if he or she could have returned the ball and the opponent has made every effort to avoid the interference.
- The player is not entitled to a let (i.e. loses the rally) if he or she could not have returned the ball, or accepts the interference and plays on, or the interference was so minimal that the player’s access to and strike at the ball was not affected.
- The player is entitled to a stroke (i.e. wins the rally) if the opponent did not make every effort to avoid the interference, or if the player would have hit a winning return, or if the player would have struck the opponent with the ball going directly to the front wall.
The main points are that a Let is awarded if the player on the ball was not able to hit the ball due to interference by the other player. A let may also be awarded the the player on the ball does not hit the ball for fear of injuring their opponent (either by the ball contacting them or the racket). it generally needs to meet three criteria:
- The interfering player made every effort to avoid interfering.
- The player on the ball would have had a reasonable shot.
- The player on the ball would not have had a clear winning shot.
If the interfering player did not make very effort to avoid interfering, or if the player on the ball would have had a clear winning shot, then a "Stroke" (and point) is awarded to the player on the ball.
If the player on the ball would not have had a reasonable shot (i.e. the ref thinks they wouldn't have made it, regardless of the interference), then it's a "no let".
I can't watch the video at the moment, but I'll try to watch it later. Ultimately, though, the ref's decision likely hinges upon the three points above.
If there is no dedicated ref, then you and your playing partner need to judge it yourself. Generally I only call "Let" (no "Stroke") when playing with friends, and only call it if I'm fairly confident I would have had a shot. My partners respect my call, and I respect theirs.