Is there a way to get that particular Doom 2 wad legally through GOG without buying Doom 3: BFG edition? I am only interested in that particular addon, as opposed to D3BFG edition.

You can't. The No Rest for the Living expansion was originally exclusive to the Xbox 360 version up until Doom 3: BFG Edition came out for the Xbox 360, PlayStation 3, and PC. The PC version of Doom 3: BFG Edition is only Doom game that legally carries this expansion's WAD file, none of the prior compilations have it (e.g. the Doom: Collector's Edition from 2001, the Depths of Doom Trilogy, the id Anthology), nor is it sold along with Doom II in digital distribution.