I recently played my first skirmish game against the AI and won playing the Raven clan. I got the proper achievement in Galaxy, but in the Profile menu in the game it says "0 games won (1 played)".
Do only multiplayer games count towards Clan Progress?

Same for me. But my first win counts and it was singleplayer too. I won several games after that, got all achivements in my GOG profile but nothing in the clan progress..

After playing a while I'm pretty sure that is a bug. Some of my wins count, some not, even if the conditions are exactly the same. Not a big issue for me, but it is the same for Conquest. Sometimes I loose all my progression and that is annoying. Saving shortly before winning and loading the saved game again seems to be a workaround. For Conquest, not for Profile.