OK, so what is the definition of instability for these Class-D amplifiers?
Stability is the same definition regardless of the kind of amplifier. It is the ability of the amplifier to resist oscillation.
Oscillation has nothing to do with whether an amplifier can double power as impedance is halved, and has nothing to do with whether or any such nonsense. Its simply means the amplifier won't oscillate.
Now one thing that potentially could muddy the waters: it is possible to build a class D amplifier that is self-oscillating. This is done using the feedback loop with the intention of using the oscillation frequency in the encoding process of the amplifier. This is a handy technique as it also allows the amplifier to correct for phase shift in the audio passband. But such an amplifier could still be able to oscillate independently of its self-oscillation if there were a design bug! Confusing- but there it is.