how this RF circuit operates

It doesn't operate..There isn't gate bias..
Or operates in B-Class with high Vin..

assume that the biasing is skipped.

If it's so, it looks like an LNA with NF optimization (Ls).
Or a kind of amplifier..

not very well. If you eve leave it biased on with a low frequency signal, the fet would rapidly blow up. You need a resistor in the drain or source.

I think it just an amplifier model。 I do not think it is a LNA ,because it has a resistor at input gate which could add noise。

It's source resistance/impedance, not an extra added resistor.
This circuit is definetly an LNA with source inductor degenerated/optimized.

just a suggestion

if it does not oscillator.
then its a class "C" pulse amp