From a physics standpoint, a "gyro" can be defined as an object whose effects due to rotational motion dominate the behavior of the object. In this regard, a rotor is a gyro because the effects of rotation dominate. Whether or not a "gyro" is a disk, or a ring with spokes, or just spokes, or a slender rod rotating about it's mid point (like a teetering rotor) is irrelevant.
To go further, at some point even a gyro is no longer considered a gyro. Take a gyro and slow it down. Any rotational effects become less dominant. Same with a rotor. Now slow it down again... and again... and again. At some point, the effects due to rotation are negligible, and neither object behaves in a manner that is comparable to their rotating states.
It's all simply masses moving around a center point. You can define "gyro" and "rotor" any way you want... but you can not imply that the same physics do not apply to each.