I'm not sure I would have confronted him in the yard like that per say, but his vigilance was top notch. If he was a LEO at the time it would make more sense to me, but if he was joe schmoe without a badge it probably would have been better to stay inside and wait for the police. At that point the guy was only trespassing, not an offense that calls for an immediate armed response outside.
Since i'm joe schmoe I probably would have been following him via windows and been armed, probably holstered though until he got uncomfortably close. I would have called the police and remained vigilant, don't think I wouldpull my gun on someone for having an illicit jaunt through my yard.