(3) A person who is not engaged in an unlawful activity and who is attacked in any other place where he or she has a right to be has no duty to retreat and has the right to stand his or her ground and meet force with force, including deadly force if he or she reasonably believes it is necessary to do so to prevent death or great bodily harm to himself or herself or another or to prevent the commission of a forcible felony.
That's the relevant section. And I'll agree it's being poorly written, poorly interpreted law, and I hope the court rejects it in this case. But it doesn't apply solely to someone's home.
The initial aggressor has no right to self defense. All this law says is "if someone is attacking you (or someone else), you can fight back." Also, if the initial aggressor does not use deadly force, you cannot fight back with deadly force.
For example, say I walk up and punch you. I'm the initial aggressor, so you can defend yourself. However, your defense must be in proportion to my initial aggression. You can hit me back, but you cannot pull out a gun and shoot me. If you do pull a gun, you lose all claim of self-defense. If I then turn around, pull a gun, and shoot you, I can claim self-defense, since you are the one who escalated to deadly force.
In a similar situation, if you are walking down a public street and see two men attacking a third man with knives, you can pull a gun and shoot one of the attackers. You are preventing "death or great bodily harm" to another person. As with above, though, if the aggressors are only using their fists, you cannot pull a gun (since fists are not considered deadly force).
Third scenario... You are walking through a woody area of a public park at night. You hear signs of a struggle, and run towards them. You see what reasonably appears to be a man attempting to rape a woman. Rape is a forcible felony, so you can pull a gun and shoot him. This last is a tad bit of a gray area because you are clearly escalating the violence. However, it does fall within the wording of the law. Though you would be better off running up and trying to just fight the man off.