[partialrecall]

"Aircraft" doesn't make assumptions about the power source. Piston engine, turboprob, turbojet and turbofan aircraft are all called aircraft despite all having different sorts of propulsion. All of those still breath air of course, but we don't hesitate to apply the term to experimental/prototype electric aircraft either. So an aircraft needn't breath air, and therefore having a rocket engine shouldn't be a disqualifier.

"Takes off under it's own power" is a qualification you're not the first in proposing, but it's controversial because it would disqualify many famous aircraft, such as the Bell X-1 and according to some (mostly Brazilians) the Wright Flyer. There is also the matter of carrier-launched aircraft that take off when the carrier is running flat out into the wind, let alone with a catapult; it's easy to say they are not taking off entirely under their own power. You could make a similar argument for rocket-assist JATO configurations, if the plane drops the JATOs after takeoff.

[vl]

This is exactly my point, records should be apples-to-apples. This particular record should go to Shuttle or similar “aircraft”. In particular Shuttle is hard to distinguish from X-15. Same thing, but more of it.

“Takes off under it’s own power and brings all equipment back” is good limitation - otherwise you can trivially design a system that drops multi-stage booster and lands tiny glider after setting a record.