Electronic – Is this part (given picture) an EM relay, relay-controller, snubber

The RC network's purpose is to provide a dampened path for the charge stored in the inductor. The MOV and TVS diode purposes' is to limit the high voltage that may appear. So they're complementary. Use both a RC network plus either the MOV or TVS.

I used 100 nF + 100 ohm for my loads for years and never had any problems so that's a couple of starting values.

This snubber circuit is used to limit dv/dt during turn-off of the switch by presenting a higher load capacitance to the inductive load usually driven by the transistor. Without the snubber, the rate would be more or less only limited by the difference of load and switch current and the output capacitance of the switch.

Besides limiting the dv/dt it also 'delays' the voltage rise, thereby limiting the turn-off losses in the switch. Of course the resistor has to dissipate the energy stored in the snubber capacitor but there is actually a point, where the overall switching losses are lower as if you didn't use the snubber at all. Here you can find a nice description of it: Snubber Circuits by William P. Robbins

It is rarely used in nowadays flyback converters because the component and assembly cost are too high in comparison to a better power MOSFET, something that is completely different in a 1200V/200A IGBT module.