Do even Texas or Arizona - two states that were part of the classical Wild West - have laws like this? I know Idaho doesn't and we do like our guns here.

The right to keep and bear arms is not the right to put a cap in your ass if you piss me off. This change will clarify that.

outside the home is whatever the common law is, which could be SYG like California and the federal level or not or some kind of duty to retreat. Can't find the precedent either way, and I have no desire to find out first hand.

In Texas, self-defense is still an affirmative defense. I have to admit to the killing and then I have to prove it was self-defense.

In FL the state has to prove that the killing was not self-defense and therefore unlawful.

In neither state do you have the ability to kill over mere anger. The classic elements of self-defense still have to be present. The dead guy has to have had the means, opportunity, and motive (as demonstrated by an overt action) to harm the defender. Absent that, it isn't self-defense but instead is murder. All SYG does is remove the duty to retreat, nothing more. Lots have people have believed the VPC hysteria over it.

of SYG, but is such a clarification helps all the better

because that act changes you from defender to counter attacker. But, I'm not sure that has anything to do with the Martin case. I can think of a case in Miami that might relate to this.
What was the previous law if there was one? Many places are based on local common law.

It dies on the vine.