Call the shots makes a loose analogy with various games, such as straight pool, where players "call" their shots. Straight pool is played on a table with six holes and 15 numbered balls. The object of the game is to "shoot" the numbered balls into the holes. Before each "shot", the player must indicate which ball they are attempting to shoot into which hole. If you successfully shoot the ball you called into the hole you called, then you can shoot again. You keep shooting until you miss a shot.
The analogy is rather loose, because in those games, the person who calls the shots is also the person who shoots. When call the shots is used metaphorically, usually the intended meaning is that the person calling the shots is giving orders that other people follow. The person calling the shots is in a position of authority, setting goals and making decisions that other people implement. The analogy makes sense at a gut level, though, because in a game like straight pool, a person who is calling his shots and repeatedly succeeding tends to project a physical posture of authority and control, making the pool balls do exactly as he says.
Watch Paul Newman in this clip from the movie The Hustler and you'll understand the analogy with negotiation in business. After he calls and makes several shots in a row, he says, "This is my table, man. I own it," (0:58) which is a very cocky way of saying that he believes that he is in control and is going to win.
The article you cite cautions against trying too hard to please the customer. If the customer calls the shots, then the customer is like Paul Newman in that film clip, and you are like the pool balls. The extra word added to the cliché, all, suggests very concisely that you should let the customer have some control, but you should also assert your own limits and expertise when appropriate.