Discrete component FM radio receiver circuit - explanation needed
Converter stages like that act like mixers because the oscillation is strong enough that Q1 is behaving in a strongly nonlinear manner.  Ideally, Q1 is operating in class A1, B or C, and only amplifying RF when it is on.  That makes it into a mixer and, if the component values are chosen correctly, it will be a mixer with at least some gain.