I had this problem, too! I figured it out today and thought I'd do some searching to help others. Just to make sure we're having the same problem...
Clicking anywhere within the room only provides a "Use Stairs" action.
Clicking outside the room results in no available actions.
The problem only occurs after certain steps in the adventure chain are completed.
Zeneport using meditation is prohibited.
I have found (after more tries than I am willing to admit) that this error normally occurs later on in the adventure chain to kill Dong Huo. The Cave is accessible when first entering China after obtaining the keystone in France.
I passed the glitch by using the eyes of Horus, which I got in Abu Simbel in Egypt. When I first entered China, I went into the cave before completing the rest of the steps in the chain and put down one of the eyes in the chamber where the keystone should go (the one with fire traps on the top floor). I then completed the other chain steps, and when it was time to enter the dragon cave again, I just used the other eye in my personal inventory to transport myself immediately into the chamber. No glitches after that. It must just be the first room at the bottom of the stairs that throws something in the game off.
To get out of the Cave after Dong Huo is defeated, you must open the door at the dragon's throat, the initial door leading to the cave, from the inside. This only feels weird because the door is usually already open when a Sim is inside, but because you cheated a little to get in, the door is still closed.
Though this worked for me, I am aware that it may not work in everyone's game. I hope this helps!
