Although it looks like you either have all information regarding where/when all events occurred relative to each other (which would necessarily give information about where/when all events happened in relation to an observer) or you have a partial ordering, which means you don't have all the information.

The partial ordering actually encodes a surprising amount of information about space-time. Specifying the temporal ordering relationship between space-time points also fixes the topological structure of space-time, its differential structure, and the metric up to a conformal factor. It doesn't let you reconstruct the full metric, and maybe you think that certain metrical facts count as "temporal facts" (which seems right), in which case the definition of B-theory I gave above should be modified to include the claim that those metrical facts are provided as well. I don't want to make the definitions too technical though, and I think the current version gets the essential idea across, so I'm going to leave it as is.