According to GOG Galaxy, I've played nine minutes of Morrowind. I've played... a bit more than that.

Is there a way to fix this? Bit of a petty complaint, but it's nice to know how long I've spent on these larger games.

In order to keep track of your time, you need to launch the game from the GOG Galaxy client, not a shortcut or from the game folder.
Also if you did the already mentioned, then there is nothing else you can do. The client is still in beta and has many problems.