I believe the 11/16" refers to the range height above the counter, at least that's the case on my RNB.

Ctycdm is correct: those measurements are for above-the-counter clearances.

Blue Star's side clearance instructions have been confusing people for years. There are at least two recent threads that discuss this in excruciating detail. When I get some time later today, I'll see if I can find those threads for you.

In the meantime, the 11/16ths measurements refers to the vertical rise of the stovetop above the countertops, not the horizontal distance away from them. You adjust the legs or casters a little taller to make the stove top height a little less than 3/4 inch higher than the counters. You can use IKEA cabinets and laminate countertops without a problem.

The 6" clearance is the horizontal distance to flammable vertical surfaces that rise above the countertops. This requirement is partly for those who might want to bury their BS range in a nook with cabinet walls rising right next to stove. (To me, that's like putting range in a closet but apparently some people have that as design preference which is the reason BS tells them the surrounding walls above the burner area should be brick, tile, metal or other noncumbustible covering.) Mainly, the 6" spacing is for people who want to put their stoves against a wall while using island trim (ie., no vent-riser/backsplash) for a sleeker looking range. BS is telling you that your RCS can be butted up against a wall if (a) you have vent-riser trim-piece at the back (a 4" riser is suffficient); or (b) have a noncombustible covering on the wall area that is above the cooktop.

Otherwise, if you want to have both the sleek looking island trim and have your stove against a wall, and you don't want tile etc. on the wall, then they are telling you that you must have 6" of counterspace between the back of the stove and the wall. That counter can be any material -- laminate, butcher block, whatever --- as long as the top of the stove is slightly higher than the counter .

BTW, if you do opt for a vent-riser on the back of the stove, you still may want a metal, etc. backsplash on the wall. The oven vents out the back through the riser. With a gas oven, you may find stuff condensing on the back wall. A surface covering like tile or a metal sheet or a tempered glass plate will be much easier to clean than a painted plaster or drywall surface.

All this having been said, BS is supposed to have good technical support, so you can phone or e-mail them to confirm what is said above.

On having a 30" hood above the 30" range: Of course, it is not always feasible to shoehorn in a wider hood, but I assume you're aware that the standard advice here is to go with a 36" wide hood. The reasoning is that the greater width increases capture efficiency which results in a good deal less frequent scrubbing of the exposed sides of the adjoining cabinets where cooking effluent otherwise condenses on its way...

Thank you for great detail, that helped a lot.
Bluestar installation manual is confusing when it comes to this, and I'm unsure why their drawings in the manual are barely visible.