How do AHRS systems meet the "gyroscopic" requirement of 14 cfr 91.205.d?
In regulations, instruments are always defined functionally. They say what the instruments must measure, not how. Any actual implementation then has to be certified, but that certification concerns with accuracy of the instrument, its reliability and ability to detect its failure – because the pilot can only handle the failure if it is obvious to them – not it's principle. So anything that can locally (without external reference) measure attitude and rate of turn qualifies.
Note that the &quot;gyro&quot; root does mean “circle”, but don't forget the other half of the word:

[…] from Ancient Greek γῦρος (gûros, “circle”) and σκοπός (skopós, “watcher”).[1]:

It means, and always did, an instrument for observing rotation, though it was only used to describe one of the methods for doing so known to the person that coined the term (that person was Leon Foucault and the other method was obviously Foucault pendulum).