Question

Do loop antennas require a ground plane?

Answer

Loop antennas do not require any ground plane, and actually perform slightly better without one.
In reality however, as the rest of the application circuitry is positioned beside the antenna  the antenna properties are effected by this proximity in terms of impedance and radiation properties. To reduce the effects of the application circuit it is recommended to fill the gaps with ground metal, this in turn effectively becomes a small ground plane.