In the timeline the Dave that became a part of Davesprite was from, Terezi tricked John to get killed so he couldn't get Jade into the game which resulted her to be killed by a meteor and so she couldn't prototype Bec into the sprite and therefore preventing the very existence of Bec Noir, right? So was there a timeline where the beta trolls' session was succesful due to the lack of stabby first guardian dogs? Or am I missing something?

Nope, that doomed timeline didn’t affect the trolls at all. Because if no Bec Noir showed up and stopped them from winning then TZ wouldn’t have ended up getting John killed and stopping the creation Bec Noir, so basically if there was no Bec Noir then their would be a Bec Noir, ya dig?