All synths except samplers have fixed initial waveforms and can be considered sample players (even Moogs meet this definition).

This is rather a torturing of the term “sample”. An analog synth does not store sampled values of a waveform in memory. The waveforms it generates therefore are not samples. Try it yourself with a schmitt inverter (CD40106), a cap and a resistor if you don’t believe me - triangle and square waves galore with no samples whatsoever.