"RF" is not a fixed definition.
RF is a matter of perspective.
Typically, one calls a circuit "RF" when many reactances (and/or transmission line effects) must be controlled to get the desired response. Often the circuit has attributes like narrow bandwidth, fixed operating frequency, constant (or a nominal range of) impedances on relevant nodes, things like that.
An "RF" circuit might be a 60Hz induction heater (in which case, the reactances are largely a matter of power factor correction for what's effectively a particularly inductive motor), or a ~1MHz AM radio (or you might argue an SDR for the same range, ~10MSps direct conversion, basically an oscilloscope,
isn't RF), or a 200MHz wideband amplifier (or not), or a 80GHz monolithic distributed amplifier, or...
In this case, it's more correct to call it a poorly coupled transformer, because there is little to no evidence of E&M delay or transmission line effects: in the near field, the impedance is low, the magnetic field dominates, and the speed of light is fast enough not to care.
But one mustn't loose sight of these things. It may act like a transformer, but that transformer has considerable self-inductance, which draws far more current than the signal. Sensing that current directly will give you quite a poor SNR. Canceling it with a capacitor instantly converts the circuit to an RF one, where there's a center frequency (Fo = 1 / (2*pi*sqrt(L*C))), bandwidth (BW = Fo * R / Zo, for series resonant), nominal impedance (Zo = sqrt(L/C)), and so on.
And as you can see, RF is a useful framework. You can instantly recite simple formulas, and apply them to the circuit. Transferring transmitter power to the coil, and recording the signal return, is easily accomplished with standard building blocks.
Tim