Interesting... chemically, stoichiometric for propane is 5:1 air:fuel, but all the sites I've visited said propane's stoichiometric ratio is 15.5:1.
And 100 - ((14.7 / 15.5) * 100) = 5.1613%
So that observed 5% difference in BTU/mile fuel efficiency may just be because propane burns leaner than gasoline. But that's only 1.3548% fuel to air by volume, well below the flammability limit of propane... so the only thing I can think is that during compression, the fuel and air are squished into a much smaller area, effectively raising the concentration of fuel per volume air, and thus bringing it into its flammability range.
As for the difference in combustion temperature, a propane flame burns at ~3596F, gasoline at ~1508F (of course, dependent upon intake air temperature and compression ratio, but from what I can find online, those numbers are typical). So the propane burning hotter would give greater thermal expansion of the air in the cylinder, thus more cylinder pressure.
But according to:
https://in.answers.yahoo.com/questio...7125444AA6w7wz
"We ran taxicabs on propane for many years. The problem is lower fuel mileage (about 15% +/-)."
So apparently the higher combustion temperature isn't enough to offset the lower energy content of propane vs. gasoline. Which makes it hard to believe it would have a higher BTU/mile in the first place.