Meningitis is literally “inflammation of the meninges”.

So any infectious agent that reaches the brain can easily become meningitis (if you are a thing that can reach the brain then if you cause inflammation you are definitionally meningitis).

So if there was a prion that caused inflammation you would have prion meningitis.

The thing that makes meningitises specifically a problem is that the inflammation itself will kill you, and the inflammation means onset is acute. Other pathogens that successfully reach the brain aren’t noticed until after they’ve caused enough direct damage to cause noticable symptoms (which is generally long after simply stopping the infection could correct the damage)

We had one patient with meningitis (bacterial) during my Zivildienst. The doctor didn't think it was meningitis until after the lab tests said so, and we all had to take rifampicine for post-exposure prophylaxis.

Fortunately, the patient made a full recovery, and nobody else (at the hospital) got infected, so at least there was a happy ending to that story.