People who sell used Macs sometimes are selling their school's or employer's computer. This is akin to theft. The real owner may have a "profile" installed to remotely manage the computer. It can be dormant for years until an update is applied at which point it requires the true owner to execute or approve the update. My guess with such an old computer is that the real owner does not even communicate any more with the computer, but the profile requires the concurrence with the central control/owner to proceed. In some instances you can ignore the message you got, but in others it prevents you from using the computer anymore.
This is why buying a used computer from an unknown source can be a problem. Apple and OWC are reliable sellers, but I would not trust anyone else.
If you can keep using the Mac, keep using it. If it won't allow you to do regular things, then if you can't contact the real owner, you will need a new Mac most likely. You can try to wipe the computer and start from scratch but even that is usually prevented by these remote management devices.
If you are in the market for a new computer but want it to be "pre-owned," OWC has a wide range of options, most with a warranty.