Dude, peter has super human reflexes and speed, he could have fucked up the dude at any given moment, guns or not, let's be real.
And exactly why he threat his family that he should have been clear with the dude and not act like a pussy.
Imagine if you had the same powers as peter and this old dude was threatening your family...
It was a well acted scene, one of the best in movie, but stupid nevertheless.
He could have just break both his hands or legs to take him out, and instead he wait even if he knows that the dude is dangerous and up to no good.
If someone die during their final fights it would be all on peter shoulders for not stopping the guy when he had the chance to do it but it was to pussy to act.