Playing as the Amazon, I've completed the first two paths, and the door to the third path is still closed. I re-ran through the first two section to see if I missed anything, but can't find anything I haven't done or killed.

I played through this entire level with Sargon last week, with no problems, but now I can't get to the final gem to finish the level.
Any ideas what I can do?

I assume you picked the two gems? Have you tried restarting the level from the beginning?

If I understand you correctly, this is not a bug.

There are three entrances—two opened and one locked.
However, the leftmost unlocked entrance splits into two paths.

The locked entrance in the middle is opened manually from the other side once you get there.