Well, going from my perspective I feel that one can't exist without another.
I started out listening to remixes of scores that I'm already familiar with, or remixes for games that I already played; then when I became aware of more games and checked out their scores the scope for familiar scores would expand.
In the event of a game you've already played (or if not played but have witnessed the BGM's presence via someone else playing it e.g. a Let's Play on Youtube), I have a tendancy to listen more for interpretation. An artist has a vision in mind, and they are sure to create that vision to match what that piece of BGM meant for them. Which in turn, would also draw in nostalgia for that purpose. Because they've understood the song even outside of a musical context, they are driven by the feelings inside to create something worthwhile for fellow fans of the game.
But if they're remixing something for a game which BGM placement for them is shrouded in mystery, it's all up for interpretation and just making it sound as polished as possible, though sometimes at the expense of cutting the feel of the original. Then if people enjoy it it might encourage a spread of players for said game and witness the original in action.
So yes, for the most part it seems to be interpretation, but in a lot of cases both that and nostalgia can exist at the same time. If we didn't have the passion for videogames of the past and present, then why the bloody hell are we here?