This is essentially correct.
George Zimmerman was a self-defense case. If the "stand your ground" law did not exist in Florida, the Zimmerman trial would have played out the same way.
Early in the case, when stories first began to circulate, Zimmerman was portrayed as a nutty neighborhood watch reject. Some people thought he would attempt to claim he used deadly force to prevent Trayvon Martin from committing what in Florida would be called a "forcible felony". In the end, at trial, Zimmerman didn't even testify. The prosecutors couldn't even prove murder BRD (beyond a reasonable doubt).
It was not a matter of Zimmerman proving that his personal space was his "domain", or that Martin had trespassed on it.
It is worth noting that "stand your ground" in the above sense -- deadly force to protect a neighborhood from a "forcible felony" -- is distinct from "duty to retreat." A long time ago, under common law, it used to be necessary to "retreat" before raising the defense of self-defense in a murder case. In other words, a defendant had to essentially prove that he retreated or attempted to retreat before using deadly force in self-defense. And in many states, a defendant actually had to prove that he was unable to retreat before being able to claim self-defense. The Supreme Court effectively put an end to this in Brown v. United States almost a century ago, in 1921.
Now, in most jurisdictions, there is no "duty to retreat" before using deadly force in self-defense. This has absolutely nothing to do with "stand your ground" or Florida or racism or handgun laws or the Second Amendment. It would be a terrible outcome of the Zimmerman case if state legislatures somehow started to reinstitute a duty to retreat in state criminal codes.

