That's pretty much how it was intended to work, yes. The Federation would be an expansive amoeba - but its defended core would be a tight little sphere sitting between the similar but less extensive sphere-amoeba shapes of its enemies, impenetrable by frontal assault. So the Dominion would go around the sphere, looking for weak spots and chances of cutting strategic connections.
If one superimposes the map seen in "Conspiracy" and later in Keiko's schoolroom onto this foldout in a similar manner, it's supposed to stretch across the foldout, too. To the extreme right of that map, there are some "loose" grid cubes of supposed UFP space, surrounding an empty, non-gridded volume where Romulus is labeled as being located. That's supposed to match the idea that the eggshell of the RNZ (the empty space in Probert's map) is surrounded by areas of UFP space. A similar dent in the grid structure close to the camera should match the antispinward tendrils of Cardassian space, and the dents in grid towards the galactic core suggest unclaimed space or other neighboring empires.
Probert of course originally did the map without much deliberation, sprinkling familiar place names where they best seemed to fit. The star labels on that map don't easily fit the positions of the real stars; one wonders if Probert used the old Star Maps as his starting point, without noticing that Star Maps feature an innocent little coordinate system goof wherein everything is said to be oriented relative to the galactic axis, but is in fact oriented relative to Earth's axis which is almost at straight angles to the galactic one...
The Okudas, however, could use Probert's map as a reference, and when the cartography of the TNG universe gradually unfolded, the Art Department supposedly marked points of interest on a map on the office wall, for further reference - but possibly always minding Probert's stylish artwork. So when "canonical maps" began to appear in the form of DS9 set dressing, they probably were a synthesis of Probert's art and the deliberations of the later Art Department.
Star Charts in turn tries to be a synthesis of that, plus bits of further trivia gleaned from all the series and movies... The foldout was deliberately scaled to work the way it's depicted above, but squeezing the Probert map into the same frame is only possible if one uses a bit of violence.
Timo Saloniemi