Yes, you're missing something. You're missing the fact that the agent is supposed to be missing. That is, we have reason to suppose that the agent will be unmentioned.
* What does that suppose to mean?
What is that supposed to mean?
Here, we see a difference between active and passive voices.
In the first, whatever that is, it supposes something. That something which it supposes is missing. How the "to mean" is meant to attach to the rest of this clause is uncertain. This isn't a coherent sentence.
In the second, we don't know who supposes, and we just don't care. To put it in the active voice, someone (maybe everyone) supposes that to mean ... and we've reach the heart of the question:
What does everyone suppose that to mean?
or maybe even
What could anyone suppose that to mean?
Anyone, everyone, someone, just you or just me -- the agent isn't relevant to the question. We have reason to suppose that the question will be cast in the passive voice.
That is to say, it is supposed to be a passive-voice construction.