Ah, I found the official answer to my question in the definitions (definition 9):

“OPERATING SYSTEM PROVIDER” MEANS A PERSON THAT DEVELOPS, LICENSES, OR CONTROLS THE OPERATING SYSTEM SOFTWARE ON A DEVICE.

This still leaves room for ambiguity, though, especially when it comes to Linux: is the OSP the person who installs the OS (e.g. a sysadmin)? They control the operating system on that device. Or are they the individual/organization that deems what software counts as a given operating system (e.g. Microsoft or Linus)? They develop and license the operating system that happens to be on a given device. Maybe it’s both, but the context suggests the latter more strongly to me.