I hate to be a jerk but that dog is not crying.
Many people have told the poster it was “reverse sneezing” but they’re so emotional and defensive they will not listen.
If they had simply held the dog’s nostrils shut briefly they would have stopped the “sneezes” and its suffering.
Reverse sneezes are generally not dangerous but they are distressing to the dog.
When dogs do cry it’s usually expressed with whimpers or howls.