The different settings are done by switching resistors or capacitors in and out of the signal path at the input. This is not that difficult as surface mount devices can be quite small, also multiple resistors can be combined to achieve different settings. As an example if you could have a 180 Ohm resistor and a 300 Ohm one. If you paralleled those two you would have 120 Ohms.
This is really the only way it can be done as the effect of the resistance (and to a lesser extent, but still audible, capacitance) is that it forms a resonant circuit with the coils in the MC cartridge that when set for the most musical perfromance performs an optimum damping of the stylus/coil/suspension resonances.
Also the entirety of the RIAA equalization is not done digitally. Although the information might not be easy to find now, when it was introduced the way the Urika 2 works was clearly explained. The first part of the Urika 2 is the same as in the Urika 1. This includes the initial gain stage (the biggest part of the gain) the high-frequency RIAA equalization and the above switching that was added to the Urika 1 circuit. So the significantly more powerful and high-frequency EQ adjusted signal is then converted to a digital stream of 1s and 0s, the bass EQ is applied, and any necessary correction to the bass and treble EQ is made. This is done because the dynamic range needed to handle the very low level signals put out by a MC cartridge and fully EQ it would be virtually impossible to handle well with current state of the art in ADC design. Giving a big boost in gain and doing the high-frequency EQ gets the level of the signal up significantly so as to keep low level noise and distortion from the digital conversion at low levels.