Can you "win" the game with the minuteman? I thought as you could only side with the BoS, Institute, or Railroad?

Yes minute men, instatute, railroad, and BoS but if you go with minute men they team up with the railroad by default.

ah ok, so at least I didn't miss much.

No, i finished for Minutemen earlier today, and the only contact with Railroad i had was for the chip. And fighting some of them on Bunker Hill. They weren't involved in the final quest in any way.