That is exactly what I am talking about. Your example doesn't "prove" separation. It's a furphy.
Continue present heading will not guarantee to keep the aircraft apart laterally. If the wind is different at any of the levels between and including FL370- FL390, then the possibilty exists that the aircraft will drift closer together until they experience the exact same wind at the exact same level (FL380). Lateral sep could be lost within those levels before vert exists.
If, however, the aircraft are told to "track direct to d" and " track direct to a" respectively, that guarantees they will remain on set paths (which is what you are seeing on the radar) despite moving air masses, and therefore known distances apart. Aircraft told to "track direct XXXXX" don't have mysterious intermediate points in their route, unless not following the clearance.
I imagine that this is an old-fashioned technique from pre-RNAV days, when headings were probably more accurate than 'own nav'.