The purpose of this article was to explain jitter and the levels at which it can impact audio signals, not a discussion of various transmission protocols like S/PDIF, AES, USB, etc. as that was far too much for this introductory article. But, embedding the clock in the signal is no problem. Most if not all high-speed serial digital links track the incoming data and recover the clock from the signal, including things like PCIe, SAS, SATA, Ethernet, USB, and so forth that transmit data at rates well above audio. Many of them transmit data in packets, short bursts of data, so the processor must perform various operations like error checking and assemble the packets into a continuous stream for the DAC, using an internal clock normally decoupled from the incoming clock (very simplified explanation). All modern audio processors/DACs buffer the output signal from the incoming data stream and generate a clean clock using PLLs as @Keith_W said. Jitter was more an issue 20+ years ago, and mainly for HDMI since the audio data stream was allowed to have fairly high jitter (10's of ns in some AVRs). Even at that level a number of processors were lauded for their sound quality; it takes a lot of random jitter to be audible.
That said, in general S/PDIF tends to exhibit higher jitter IME, at least partly due to the internal ICs that capture the signals and do not provide a very low jitter output. That is not something I follow, but several members have noted that some integrated chips that include S/PDIF inputs do not do a good job of suppressing jitter. I have a vague memory of seeing 100+ ns of jitter measured for a popular S/PDIF receiver chip some years back. I could not say how audible that is but it's high. I suspect the error rate is also fairly high and that may be a bigger sonic issue than jitter; again, I do not know for sure.
That said, in general S/PDIF tends to exhibit higher jitter IME, at least partly due to the internal ICs that capture the signals and do not provide a very low jitter output. That is not something I follow, but several members have noted that some integrated chips that include S/PDIF inputs do not do a good job of suppressing jitter. I have a vague memory of seeing 100+ ns of jitter measured for a popular S/PDIF receiver chip some years back. I could not say how audible that is but it's high. I suspect the error rate is also fairly high and that may be a bigger sonic issue than jitter; again, I do not know for sure.