It's relevant to the crime because murder requires intention to kill - mens rea, the "mental element" to the crime. He'd said he would kill any burglars, and he said he hated gypsies and would kill them too. That's intention, which removes it being purely instinctive self-defence (which is, rightly, legal).
You're wrong on the law, incidentally. The test of reasonableness is fairly subjective, which is why the Tory Party dropped plans to alter the law to make it "grossly disproportionate" force, instead of reasonable. And even under that change, he'd have been found guilty, because it was plainly disproportionate.
And if we're talking breaking the law... he was keeping a pump-action shotgun in breach of it. His license had been revoked. That's a crime, too.
Obviously, if a burglar breaks in and is stabbed/smacked over the head with a bat/shot while still in the house and scaring the legitimate occupants, and dies, then tough luck to them. But that isn't what happened here, not by a long shot. He wanted to kill the intruders and he did just that. Not legal, and not right. The kid was a crim, but he was also a 17 year old. He's been dead decade, yet he would only be 27 now. He was a human being, and while he was probably headed on a life of crime he was also a son, a brother, a cousin, a friend. He will have had people who loved him, who will have been devastated. He didn't rape anyone... or kill anyone. But he was killed. If that had been in genuine self defence, again I'd say tough, poor life choices and sad outcome. But it was not.
I'm not going to reply any more because this is just pointless. People are coming into this with their minds made up and not really engaging with what happened. When I first heard about the case I supported him too, but learning the actual facts made that impossible. You can't decide you're going to kill anyone who breaks into your house (and sleep with a loaded gun next to you, fully dressed, with a series of booby traps set to delay an intruder's getaway) and expect to get away with it when you succeed. That's light years away from a terrified person striking out to protect themselves and their family, which is why the second is legal.
Everyone knows about the Tony Martin case because convictions like this are so exceedingly rare.