When someone has food stuck in their esophagus it can be an emergency if the person is having trouble breathing.
If the person is breathing properly and coughing then usually coughing hard enough can dislodge the food from the esophagus and the person will be fine.
It has happened to me and I just coughed hard for about a minute which seemed like days and eventually I coughed up the food and was not choking.
If the person is actually choking on the food in their esophagus then call 911 and start trying to dislodge the food by giving them the heimlich maneuver to dislodge the food.
But if the person is still able to cough and talk some and is breathing fine then there's not much to worry about.