They knew fully well he was a nut and not an actual threat. They didn't care. They executed this guy and left his body lying in the street - perhaps as a warning.
What warning were they trying to send? "Don't post things on social media about how you might assassinate the President?"
I'd imagine they get lots of threats like this one. The Secret Service then goes to the house, knocks on the door, and asks to talk to the person so they can assess how much of an actual threat they are. I'd bet most people in that situation just open the door and talk to them because they realize "oh crap, I screwed up, I shouldn't have said all that crap."
But I'm not sure what generally happens when someone threatens the President and then barricades themselves in their house when the Secret Service comes to question them.
My guess is that they don't just walk away, but I'd be interested in seeing what the protocols are supposed to be. Threatening the President is a crime, so they do have the right to arrest you and take you into custody.