Yes, it is in reference to time. Why? Good question. Perhaps, it comes from a short order cook, who generally work in diners. They get "short orders" and they prepare food quickly.
People go to a restaurant and try to get their food in 20 minutes. Are these sorts of orders considered "short orders"? Do you call these sorts of orders "short orders"?
The orders are understood to be short because of the type of restaurant. In a diner, orders are generally short and simple and therefore, the cooks are "short order cooks.
However, this is just a convention. If I go to a fancy restaurant, and order a bowl of soup, the order is short but it will not be prepared by a short order cook. It will be p