I would argue that an RF mixer and an Amplitude Modulator are one of the same thing.
Consider two frequencies F1 and F2 (where F1 > F2) as the input to a mixer, the outputs will be F1, F2, F1+F2 and F1-F2. Filtering on the output of the mixer will select the required component, (F1+F2) or (F1-F2) and suppress the others.
In an amplitude modulator, let the carrier be F2 and the modulating signal be F1, the outputs are F1, F2, F1+F2 and F1-F2.
The filtering on the output of the modulator is tuned to the carrier frequency F1, but as the side frequencies F1+F2 and F1-F2 are close to the carrier and well within the passband of the filter the outputs are (F1-F2), F1, (F1+F2).
We could rewrite this as (Fc-Fm), Fc, (Fc+Fm) where Fc is the carrier frequency, and Fm is the modulation frequency.
Going back to the OPs original question, one of the signal sources is in series with the emitter and so will change the "bias" of the transistor resulting in AM modulation.
I also see that the AM waveform is somewhat distorted.
As an afterthought, if the filter on the outout of the mixer has a narrow enough passband, it can select just the (Fc+Fm) or the (Fc-Fm) resulting in a single sideband signal.
(But lets not go there otherwise AG will go off on his hobby about quacking ducks! ;-) )
JimB