This description of the word "diet" is overly simplistic and marketing centric. A diet is just the schedule (list) of foods consumed, as in "I have a terrible diet" or in "pandas exist on a diet of bamboo shoots and leaves". This term is overloaded in areas like the weight-loss industry to refer to voluntary limited intake, but it's still a diet as in an enumerated schedule of specific foods. "Going on a diet" is often used in the context of specific health goals as distinct from the normal "diet".

There's an episode of Mad Men where they are coming up with pitches for weight loss products and losing weight is referred to as "reducing", a term from before the word "diet" was used as you've described.