I have the vague idea I could try to do this with some kind of chisel, but I have no idea how to get started or if I'm even barking up the right tree. Any pointers would be much appreciated.
You could do this using a gouge (a type of chisel with a curved cutting edge) but it would require that its edge be very sharp indeed* to get an acceptable surface inside the scoops. In addition to getting the gouge sharp enough initially this will require frequent upkeep of the edge during the job, as often as every few minutes depending on the hardness of the wood and how well it is cutting.
Freehand routing with a round-nose bit might achieve this but it would require unerring attention on the part of the operator O_O
In either case some practice pieces will be required! Even with that I wouldn't expect to get a really nice result first time.
*Sharpening a gouge to an equivalent level to a straight-edged chisel is something that many find much more difficult, some guidance that will help achieve the necessary sharpness (there's really only one standard to aim for, hair-poppingly sharp) is given in a previous Answer, How do I sharpen curved tools like gouges?
I believe you will find your answer here:
Custom tools were used and a lot of time. Best way to replicate would be print out a similar patter (or copy his). Trace it onto the surface and start carving. You will be carving out the lines and leaving the raised sections. Then, if you want to speed up the process. Use a rotary tool like a Dremel.