He was able to protect his family with no one getting shot and without presenting the BGs with the tool to kill him and his family outright.
Yes he was able to save his daughter (his goal) but now he may die or have permanent injury. They already had the tools to kill (he was attacked with them) so giving them another tool to kill is moot. A firearm would have given him the ability to stop the attack without getting hurt.
He was acting on his fatherly instincts. If he had done the same (unarmed) to save a stranger I would admire his bravado and point out his lack of brains. It is foolish to engage multiple large men unarmed unless you are throwing yourself to the crocodile to save your loved one.