It appears that the study was considering the shuttle's ability to glide while re-entering. They were afraid a shuttle could launch from Vandenberg and do a maneuver similar to the shuttle's once-around abort and approach the USSR from the south (most of their early-warning systems were facing north) and possibly even return home afterwards.
It's a cute theory but you should be skeptical of the claim that this study was the motivation for the Soviet shuttle program.
The main thing necessary to understand Buran is... why the big heavy delta wings? It is clear why the US shuttle has them: Reference Mission 3A/3B, which the USAF added to the design requirements in exchange for political cover in Congress (see T.A. Heppenheimer, _The Space Shuttle Decision_). If you launch due south from Vandenberg and you need to return back to your landing site (either because of the Reference Mission or because of a Abort-Once-Around) you have to be able to move roughly 1/16 of the Earth's diameter in the atmosphere (otherwise you end up in the Pacific Ocean), and that forces you to the big heavy delta wings that sacrifices a lot of payload.
But why did the Soviets need that much cross-range? First of all their spy satellites were not generally put into polar orbits (they used shorter lived satellites that didn't need sun synchronous orbits) and second of all, one polar orbit around from Baikonur runs right over Russian land rather than the Pacific Ocean, so they had no need for all of that cross range.
The only thing that makes sense to me is that a design goal for Buran was "copy the STS, but don't do quite as many silly things" because I simply can't find a use case for that much cross range for them.
I would be willing to bet there are political considerations at play also.
The popularity of the Space Program in America has fluctuated over the years with a corresponding amount of support and funding from the government. That being said, the Space Shuttle was seen at the time as a major iteration in space technology. Moreover, it closely resembled an actual "space ship" from science fiction lore! For the first time space technology was recognizable and relatable to the American taxpayer.
They probably could have accomplished more with a less iconic design, but they would have had trouble selling it to Congress and taxpayers. For a society that's used to seeing billion-dollar metal tubes used up every several minutes before exploding into the ocean; the reusable "Space Shuttle" was a comfort investment for Americans that boosted confidence and enthusiasm for the Space Program.
Delta wings aren't necessary for that. The Soviet's wingless first/early iteration of a Shuttle copy was designed to soft land with its 20 ton return payload by parachute, aided by retrorockets firing at the last moment.
I mean, the Soviet version of the B29 had extra rivet holes because one of the B29s they reverse engineered had a manufacturing mistake. Would they trust their engineers to make a close copy that wasn't exactly the same aerodynamically? I know that's in a different era of the USSR, but still.
When you encounter things you don't understand in complex engineering it's not unwise to copy them because you are either copying a harmless mistake, irrelevant appendix type feature or it's a key feature you don't yet understand.
Plus the cost overhead for a few more rivets isn't crazy; even if they're superfluous and you know it, better to spend brainpower on more complex and critical engineering.
The idea was to just dip your perigee a bit into the atmosphere, use the aero surface to change inclination, but not loose enough speed to put you apogee into the atmosphere as well.
Voila, you are now in completely different orbit, one that a conventional spacecraft can't achieve due to the delta-v requirements an inclination change would require.
Also once you have don this, you can put your perigee above the atmosphere by a short OMS burn.
It's a cute theory but you should be skeptical of the claim that this study was the motivation for the Soviet shuttle program.