Fresh install on a PC, and when I load this game, it asks me to insert a disc... I press Cancel... then it only lets me play Multiplayer?

Win 10 Pro

What gives GOG?

GOG support is not very likely to see your question here so you should contact support directly as this is easily fixed but it should not be so that every new person who installs the game has to do it themselves.

This is most certainly a problem where you do not have a dvd drive at all. This can be fixed by mounting ANY file as a dvd. I use a text file (done with notepad or similar) with the single word 'dummy'. That way it takes hardly any space. This seems to usually fool the program into believeing you have a dvd drive.