Okay, I know it's probably the least important thing about the craft, but still...
Why are they using such an ancient, decrepit-ass rocket motor? The AR2-3 is incredibly old - it dates back to a Gemini-era trainer, basically a modded F-104 that NASA used for early tests and training for spaceflight. It was made back when rocket chemistry was still in the "even the experts don't know much" stage, so it burned jet fuel and high-test peroxide (90%+ H2O2 in H2O).
Jet fuel is not good for rockets - basically, the restrictions on what compounds can be present is fine for jet engines, but leads to horrible problems with rockets. There's a specific petroleum-product blend designed for rockets, called RP-1, which clamps down on things like sulfur compounds or alkenes that love to gum up the works. This rocket was originally used on a jet fighter and shared fuel with it, so that was understandable... but the USAF recertified the engine for modern JP-8 instead of the old JP-4. So they already went through the effort of making it work with a new but similar fuel. Unless the X-37 hides a jet engine on itself somewhere, I don't see why they couldn't have used RP-1 instead.
Further, rocket science moved away from peroxide for a reason - it's dangerous. It will explode for basically any reason - peroxide decomposes exothermically, so once it starts reverting to H2O + O2, it's nearly impossible to stop. And it reacts with tankage surprisingly often. Oh, and it does horrible things to your specific impulse, which really hurts you on a last-stage engine like this one.
Honestly, using the engine at all is a weird choice. Sure, maybe they had some laying around... from the sixties... but that's like putting an F-104 engine in a prototype aircraft, it just doesn't seem right when other off-the-shelf systems work better. An AJ-10 would have worked beautifully. An RL10 might not have fit the aero package (hydrogen is a bulky fuel), but would have given them some impressive dV if they wanted it. Aestus would be a perfect match as well, if they didn't mind outsourcing to the Euros. Even Kestrel would work (although it first flew around the same time as this, so understandable not to use it). Point is, they had options, and being the Air Force, they could easily have just had an engine custom-made for it if they so wanted.
So what are the implications? All I can think of is a) they don't care how badly the rocket performs, b) they probably aren't going to keep that engine in whatever "production" version they build, or c) they have some other reason to use peroxide or JP8. Maybe peroxide is also their monoprop for RCS? That isn't really worth it though, particularly when UDMH works better as RCS and in the main motor.