That is not an example of vigilantism at all even if he is not a police officer.
So what would you call it?
Someone not trained to assist someone who is trained and doing their job, isn't very wise unless it's life or death.
I wouldn't let a person who isn't a law enforcement officer assist me, especially armed. If they want to assist so much, join the force. I don't know them, their intentions, or anything at all.
I asked the OP that I quoted for his reasoning. As I do not know, maybe he was off duty?
Regardless to add. He was with his wife, who most likely was in the line of fire as well. For what? A breaking and entering? Is it that worth it?
Leave it to law enforcement.