Because it's using both. Or neither.
Within a cycle, L3 maintains fairly constant supply current. This feeds TR1/2 and C9-C11 capacitances without extreme peak currents (well, give or take how TR1/2 switching goes; when tuned for an inductive or resistive filter input impedance, it should be alternating flats and sine humps, as a traditional Baxandall oscillator has, and the current will be steady).
Over many cycles, L3's DC voltage drop is almost zero, so it tends to enforce a constant output amplitude (at the inverter, not necessarily so after the filter). So if there is suddenly a heavy load (due to some sort of mismatch, I suppose), current ramps up and up and up to maintain that voltage. Conversely, if load drops suddenly (opposite sort of mismatch?), the voltage on TR1/2 shoots way up. Both can easily result in blown transistors.
It's a wide open loop, with neither current nor voltage protection -- not even having a current limited supply or TVS voltage clamps!
So, for purposes of filter design, it is current mode.
For purposes of amplitude, it is voltage mode.
For purposes of switching and safety, it is open loop.
Tim