Well, they're definitely not players. I see what you mean that they're, in a sense, their trans-scratch selves... But they're really separate characters. Dave is not Dirk's Bro, they're just genetically identical.
But if Darkleer isn't Horus, and never played the game, how does he live under a void veil? I can't remember where the heck I saw this, but I swear someone in-comic described the game's classpects as challenges tailored to each player. Which almost suggests that the game doesn't grant them superpowers. Maybe Dave didn't get his understanding of time from playing SBURB, he always had it (he did mix beats as a hobby). The Alchemy just let him make the turntables to act on his existing power. Likewise Dirk's weird soul-ripping ability and Aranea's sight-healing power would be things they always had the potential to do, the game just forced them to develop those powers more.
As Liber Celi pointed out, some of the Alternian troll ancestors exhibited powers or affinities similar to their Beforan genetic clones. There are bits of evidence that the beta kids' ancestors did too:
Mom, Rogue of Void: As pointed out, appears from nowhere:
http://www.mspaintadventures.com/?s=6&p=002131Bro, Prince of Heart: Overwhelm's Dave's personality at first. Murder-porns puppets...
Nanna, Maid of Life: Saves John's life by spawning a bed, lived with the Batterwitch (also Life-aligned?). Only Beta kid ancestor who was brought back (except grandpa??).
Grandpa, Page of Hope: I have no idea. Page and Hope are weird. I still don't know how he was hanging around on John's planet though.
So yeah, non-players are distinct from their scratch-clones, but they often exhibit the same affinities and powers as their identical clones. They don't have titles, but if they DID play the game, they might get the same titles (or at least the same aspects).