No it's not satire or parody, it's trolling, plain and simple.
And the way to respond to it is the way you respond to any troll on the internet. It's the same strategic pattern.
Yeah, the American people elected this troll to be president knowing full well what they were electing. So the important thing is to respond to the folks who empowered the guy.
But Trump himself? It's the old internet adage: don't feed the trolls.