Again, before listening to Luis Miguel's version, I highly recommend that you hear the original, recorded by its composer José Alfredo Jiménez in 1963. Jiménez was one of the great ranchera composers and performers in the 50s and 60s, a self-taught songwriter of proletariat origins who contributed immensely to the Golden Age of Mexican Cinema, producing a body of work that few songwriters anywhere have equaled in scope and quality.
This particular song takes a bolero form (the punctuated guitar rhythm is what gives it away), making it even dreamier and more classically-minded than usual for ranchera, and ranchera is usually one of the more dreamy and traditional Latin genres. Luis Miguel plays up the classicism, holding the power of his voice mostly in check throughout. As I've had occasion to point out again and again, he's a singer of consummate skill: here, the quality of power held in reserve mirrors the lyric.
"La Media Vuelta" translates literally as "The Half-Turn," and it's a term borrowed from the art of bullfighting; the media vuelta is a method of sticking the bull that requires perfect agility and timing — like a dance, which is the other use of the stock phrase. The singer of "La Media Vuelta" is renouncing his love for her own good; all the power in the relationship lies on his side, as he admits when he says "yo soy tu dueño" (a tricky phrase which translates as "I am your lord and master," but connotes something like "you're so in love with me that you'll do whatever I say"). The sentiments are horrific from a feminist point of view — dude's just dictating to her regardless of her own wishes, can't they sit down and talk this out? — but as a representation of a certain floridly Romantic scenario (it's all a bit Mr. Rochester), it's an effective character portrait. He's aware of the damage he's doing, but power is its own reward.