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.
The problem: The guy is equating
continuous time with
analog. It's not. Note that we can't really store numbers, they're abstract. We can write down symbols on paper to represent them (the world settled on a system developed by Indians, spread by Arabs; Mayans, Romans, and others did it differently), we can store "analogs" of the numbers (more to follow). If we want to transmit them over a wire, we encoding them in a continuous time signal. We design the encoding so that it's robust and will survive some degradation.
Encoding notes: Computer memory stores levels (per bit), which will vary and can produce errors (rarely), they have built-in error correcting. SSDs might encode more than one bit per cell, using more than two levels. CDs players have to measure reflectivity in pits, which will not reproduce identically for every "bit", and it may be read at different rates. In fact, there is so much chance for errors (less rarely than memory) that there is robust error encoding built in. There are many ways to do it over wire (SP/DIF, USB, etc.), but the bottom line is usually that it's usually either with an inherent clock, or one that's recoverable from the signal, and it's discrete levels that gives noise immunity.
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.