The actor who plays Doug broke both his heels in a ski jumping accident. This was written into the show to keep the character around and, as described on the DVD commentary by creator Bill Lawrence, "We felt that breaking both of his feet was a very "Doug" thing to do, so we decided to write it into the show."
When Dr. Cox starts the Heimlich maneuver, he only does one thrust before he says he can't clear the man's airway and yells "call 911!" Anyone who is first aid/cpr certified, especially a very experienced doctor, would try more than once to dislodge the food in the choking victim's trachea, before resorting to cutting a hole in the man's throat.