There is two parts to "real time"
- Continuity: the system can takes in a continuous stream of samples and puts out continuous stream of the same rate. This can go on forever: no samples are lost.
- Latency: that's the delay that the processing introduces and the delay between the input and the output streams.
PCs can certainly do continuous real time processing . Typically PCs don't process one sample at a time, but they buffer up a larger number of samples, process them in one go and than output a full buffer again. That's how they get around the "OS is doing a lot of other stuff at the same time" constraint.
However the buffering introduces a lot of latency (100s or 1000s of samples for audio processing). In many cases this is not a problem and in other cases it is.
The article requires a sign-in that I don't have, so I can't read the full thing. I'm guessing that they have a feed-forward real time processing part that is updated in non-real time using some supervisory process. Feed-back cancellation requires extremely low latency and you can't do it on a PC. Note that they also call it "Control" not "Cancellation", so it may be something different than ANC headsets or ear buds.