It sounded like there was visitation for kids involved, and the chap with the gun was not a parent. Likely this issue had surfaced before. But as for self defense, the shooter backed off, went into the house and returned with a weapon. No blows had been exchanged at that point, no need for a gun. The shooter brought it and reengaged in the dispute. Not self-defense, but murder.
As an aside, that could have been handled better all around.