I don't get it.
Is he claiming this soldier is responsible for the bombing at his "church"?
No. Phelps is complaining that he doesn't get enough attention.
You don't get it because you are a normal, rational, and sane human being.
I only got it because I supervise a truly deranged person, and that experience has given me great insight into the minds of people like Phelps.
Phelps is saying that God killed this US Soldier because someone bombed Phelps' church in Kansas.
The "logic" goes like this:
Some bombs Phelps' church.
That makes God mad. (Because God is on Phelps' side)
The US Government was somehow behind the bombing, or the US Government failed to aggressively pursue and identify, and arrest, the bomber.
So, God avenges the bombing by killing a US Soldier.
See?
If you are deranged (and/or if you have a very warped theology), this makes perfect sense.