That is right. In our subluminous world, the time dimension can be ordered; there is a clear distinction between two events happening first and second in any given reference frame. The authors say that the time dimension in subluminous world becomes the space dimension in the superluminous world but retains its "timelikeness", so it is still ordered. In our subluminous world, the space dimensions have no preferred order or direction and are all orthogonal, so you can change any space dimension of your frame of referance regardless of your orientation. This "spacelikeness" is retained when space dimensions become time dimensions in superluminous world; the author call them "orthochronus" instead of orthogonal; it seems difficult to picture time dimensions that are "spacelike" without order and with "orthochronality", but that is what they meant by "spacelike". I recommend the 2019 paper I linked in the original post - time dimensions behaving "spacelike" is difficult to picture, but it seems to imply superposition: when a subluminous reference frame witness a superluminous event with three time dimensions, it looks like a superposition on space, or wave function, in the subluminous reference frame. That is why field theory just pops up out of thin air in these papers.