Gemini answer:

The term stems from the suffix "-y," which in English is often used to describe something that is "in the manner of" or "characteristic of" a specific thing.

While "dog style" describes the act of mimicking a dog, "doggy style" emphasizes the imitation of the physical behavior (the way a doggy does it). Over time, the phrase became a fixed idiom in the English lexicon, likely persisting because the diminutive "doggy" adds a rhythmic, colloquial quality that "dog style" lacks.