At first I felt <shrug> so the he wants to refer to it as analog. But OK, words have meanings, let's think about why this is wrong.
Digital means numbers. It doesn't mean sampling or discrete time, although digital lends itself to discrete time and not to continuous time, so we can assume digital implies discrete time.
Analog implies something that is analogous. The rise and fall of the voltage level is analogous to the compression and rarefaction pattern of sound in the air. Clearly, it pushes a speaker to create those exact compression and rarefaction patterns.
Close but I would quibble with the definition of digital.
Digital is about representing information as
discrete states, nothing in between the states. Can be binary, trinary, or whatever. Not necessarily numbers. In fact, numbers can be a continuum (rational numbers, real numbers). Digital states may be represented as discrete numbers, but they don't have to be numbers, and numbers are incidental. The essential point is that the states are discrete.
Analog implies a smooth continuum of signal. Not discrete, but any of infinitely many values within a range is valid. Note that this does not imply that analog has infinite resolution. Some states are so close together they cannot be differentiated.
You said analog means a representation that is "analogous" to the information being represented. This is true. Yet all our senses are perceptually "analog" -- regardless of whether the universe is actually analog or digital, smooth continuous is how we perceive it. So as a consequence analog ends up implying smooth continuous.
... Such a signal over wire is not an analog of the sound. It does contain analogs of the numbers, though. While I'm not mad at anyone who wants to call a continuous signal "analog", it's pointless and causes confusion. Since digital is always encoded in some way, I don't think it's helpful to call it analog when it's a voltage over a wire and digital when it's not. It's still encoded digital. And since digital is always encoded, drop it and call it a digital signal.
I agree. You can have media that stores a smooth continuum, like gradations of magnetic field strength. If when reading it, you apply thresholds to force it into discrete values, then you've "digitized" it.