Right.. I've now completed the first mission in the Chinese campaign a couple of times but the game won't let me proceed.
Every time I finish the mission, I'm put back to its briefing where I can restart it or leave. The next mission won't open in the archives either.
The original campaigns and the Black Dogs campaign work perfectly. Is the Chinese campaign just 1 mission, or am I missing something?

You cannot start current missions from the archives, only completed ones. If the first mission is showing in the mission archives, you should be good to go on the second one from the mission briefing screen.

I know, the problem was that even going directly from the start screen to the campaign, completing mission 1, the game only gave me a "End Mission" option at the end of map 1 rather than the standard "Next Mission", and just sent me back to the first mission in an endless loop. That did the trick. Thank you!

Ah, cool! One more new thing to learn. Thanks, Ded10c!

Interesting. I had the same problem with the Red Brigade campaign. Clicking on "End Mission" on the mission summary screen after the first mission brought me back to the main menu and choosing the Red Brigade campaign still showed me the briefing for the first mission.

I had saved on the mission summary screen and reloading that save fixed things. "End Mission" lead me to the next mission's briefing that time.

Curious.