I think that means nothing flammable 12" to the sides of the cooking surface measured horizontally or vertically. It does not refer to the base cabinets or anything else that is not higher than the range itself.
I would not recess the stove into a deeper wall cavity to keep the oven door flush with the cabinets, as during the clean cycle the door itself gets plenty hot.
Casey

that's correct. it is of course acceptable to have a range meant for residential use up against a wall and flush against cabinets on either side. thousands of people have installed them this way.

Yes, but there are a couple of definitions of against the wall. If you mean in a corner against a wall, that's completely undoable. That's where that 12" minimum clearance come into play. You need 12" from the side of the range to that wall, and it had better be fireproof (tile or stainless covered) and have a real exterior exhausting 1200= cfm hood above it for a successful installation of a pro style range with a grill. Grills don't play well in most homes without a lot of air leaving that home, which translates into makeup air and a ERV for most high CFM venting. Even without a grill, you'd still need a really good vent to the exterior just for the burners.

The range would be installed in a corner, and our bldg would not permit exterior exhaust, so I guess that knocks this range out of the running. Any recommendations for an apartment-friendly comparable? 36", dual-fuel, under $7K? I really appreciate the assistance - thank you.

If you do not have exterior exhaust at all, you should focus on electric. You might consider induction.

BTW, the requirements for that range are very similar to pretty much all "pro" ranges that you're likely to come across. It's not unique to GE--it comes from the need for safety when you have 70-100k btu coming off of a stove, and cabinets/wood anywhere above that stove.