He could have died from what's called "Positional Asphyxia". There are more than a few cases where people in police custody have died from such a condition. He could have gotten stuck in the pet door, and while trying to fight his way out, struggled to the point that he got into a position where he couldn't breath properly, and basically suffocated from fighting to get out.
If I stand on your chest, you'll likely be just fine for quite a bit longer if you lay still. But if you struggle and fight, you're going to find yourself out of breath faster. It's a horrible way to go, and I feel for the guy. But at the same time, he probably shouldn't have tried to crawl through a hole that is around 8x8 inches. I've gone through dog doors in the past to get to people who need help, but if I don't think I can make it through, I'll find another way in, you know?