It wasn’t even his house; it was his girlfriend’s. She thought they were trespassers, she called him for help (she also called the sheriff) and he showed up pointing a gun.
They also were in their car outside the gate to the property. TECHNICALLY that gate may be inside the property line, but that's still totally egregious.
Like, we have trespassing laws here in Europe as well, but I have never heard of anyone taking these as serious as some Americans seem to do. Worst thing to happen if someone is found to trespass would be a monetary fine.
You also have "freedom to roam" laws. Or at least in the UK.
Even in the US, no reasonable person would think someone going up to the door would be trespassing. But these kids did more than that, they hopped the fence and walked around the house. That could definitely be trespassing.
That said, it's absolutely no excuse to shoot them. At most you say "hey get off my lawn".