There are 3 parts to the project. A transmitter, receiver, and digital volume control. That might be a lot for a "beginner project" and in general, I wouldn't recommend copying an existing project unless understand how each part works.... If you have a problem you'll have to understand it to troubleshoot it... So, build & program it one step at a time... I'd start with volume control (under software control) and add the remote after the basic function works.
You can get digital pots.
There are 3 types of digital interfaces for digital pots: Serial, Parallel, or Up-Down. To me, a simple up-pulse or down-pulse seems the easiest to program and appropriate for a volume control where you don't want jump suddenly to a new setting.
I don't understand the extra taps on the volume control. I could be for [u]loudness compensation[/u] which was common at one time, but is no longer "in style". I'm sure that could be implemented with digital pots I don't know how it would work in your existing circuit.
Personally, I wouldn't recommend using a motor to turn a mechanical pot. But if I was using a motor, I'd use a servo motor NOT a stepper. A servo motor is an angular motor (it doesn't turn 360 degrees). It has a driver circuit built-in and built-in positional feedback (so it knows where it is and where it's trying to go) so you just apply power and essentially send it a "go to angle" (actually a timed pulse).
With a stepper motor, you need a driver circuit and you generally have to know where you are starting, although for up or down (clockwise or counterclockwise) you wouldn't have to know where you're starting, you only have to sense the end-points so it doesn't go too far.
NOTE- With a digital pot, you'll need to simulate the approximately logarithmic taper of an [u]audio pot[/u], otherwise it will be too loud at the half-way point and the adjustments will be too sensitive at the quiet-end. But, that's trivial in software.
If you can "break into" the signal where there is an approximate line-level signal (probably at the volume control) you may be able to wire-in something like [u]this[/u]. There might be impedance issues with tube circuits, but the odds are good that this could work.