If you go back and read through the info on the player again you will see that you can listen to a CD at the same time as it is being "saved to the HDD", which kinda indicates that they are encoding at least in real-time, and probably faster.

(list 6284, Mk1 S/N 00299 4GB blue [for sale]. Mk2 S/N 080000094 6GB blue)
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(list 6284, Mk1 S/N 00299 4GB blue [sold]. Mk2 S/N 080000094 20GB blue)