Fuzzrocious (hand made guitar/bass pedal dude) gets all of his PCBs from Gold Phoenix ( http://www.goldphoenixpcb.com ). Would be worth checking out.
In general, I'm sure if you search some guitar pedal maker forums you would get even more recommendations as the community is pretty big. If they sell PCBs for pedals I'm sure most companies would make other PCBs as well. Minimum quantity may come in to play as with any printing. Here's the one pedal DIY forum I know about if you want to poke around - www.diystompboxes.com/smfforum
I set Seeed Studio Fusion as my default pcb manufacturer https://www.seeedstudio.com/fusion_pcb.html
It's a company based in China, and I've had several boards made there. The price is cheap, the quality is good, and shipping time is excellent.
Others have already mentioned all the PCB manufacturers that I've heard good things about, but I did notice there's a bit of a hitch in the pattern in the video, the bottom half of one column of LEDs doesn't light at first (3rd column from the right)