I would say silence does indeed meet this definition.
Not to say I agree with your dubious attempt at bringing 'silence' into the fold of 'resource'.
When you start mining silence by the barrel from deep space, then we can start treating it as a commodity resource.
Also I'm not sure "zero sum" is the same thing as "limited". The former imposes stricter requirements.
I'm sticking to my guns on this one.
a) I don't know how you'd measure 'all the quiet' to determine that I'd consumed all there was.
b) even if I did, it doesn't prevent you from consuming as much (up to all) of 'the quiet' as you wanted, too.
Which brings us back to why it's not a tragedy of the commons, and why the analogy doesn't work either.
Not to say I agree with your dubious attempt at bringing 'silence' into the fold of 'resource'.
When you start mining silence by the barrel from deep space, then we can start treating it as a commodity resource.