That is the task of the resonant tank circuit, to
maintain the RF current flow throughout the device during the
off period.
During the off period, the drain volts have to fly up to
2.Vdd to keep it operating linearly, and the resonant network
has to ensure that happens.
The concept is quite standard, used for most bipolar and
FET output stages at low power (watts, tens of watts) at
VHF and UHF. Although I've noticed that modern FET
amplifier modules do run at a higher standing current and
lower efficiency than bipolar ones. All the old valved SSB
transmitters of a bygone era use that topology
I may need another long walk to ponder in more depth ...