I could see using something like this to provide electrical power to a battery pack, similar to a hybrid with the exception that the engine has no connection or intention of providing direct mechanical power to the drive line, only to provide electrical power generation. An application where it could maintain a constant RPM regardless of the vehicles situation at the time, the battery gives more energy than can be generated by the engine at any given time, and the system charges while demand is less than the engine provides.
In my opinion that would be the only way to take advantage of higher efficiency while still dealing with something that has no real grunt power. Electric motors can give all the torque you'd ever want, but that little engine could never generate it all at once.
I'm thinking of something similar to how trains and ships are powered by diesel power plants that provide electrical current for motors to do the actual grunt work.
The problem is the amount of energy required at any given time is probably going to max out the little axial engine, so you won't have ample enough durations of low demand for it to catch up with. Normal operation will be drawing on your surplus all the time. Also energy storage in itself is hard to come by, either it's really expensive, or weighs a ton.
Some people seem to think a lot of us gear heads are overall against progress when it comes to power plants, that we only want to suck petroleum gas into huge engines. I don't think that is the case at all, we just want to actually have power and aren't willing to give it up on a whim, show us a better way to get loads of power, and I bet most would be on board. (But I'd so miss the rumble of a gasoline engine.)
I'm all for alternative fuels and methods, but I have an exception, it actually has to work, and work reliably, before I want it. If I could get better performance than exists already out of an alternative power source, for the same expense, I'd be all over it.