I played and beat the second game first and really enjoyed it, and was confused when the third game was nothing like it. However, upon playing and beating the first game, I now know what that "BTNverse" in the corner means.
Well, I still don't know what the BTN part means, but I know what you mean by a "verse". These games aren't the same genre, but they tell the same story as part of a connected universe. This only make me curious what the third game is like based on the description I saw and what little I played, because if it has anything to do with these cosmic forces trying to destroy and recreate the world, I'm definitely trying again to see what happens there.
I swear I recognized one of the monsters in that third game here...
That's another thing, by the way. It was really satisfying going back to this game and getting that "oh, that's what happened!" feeling. Playing the character that ends up destroying the world in the second game is super cool. ^^
Of course, yes, this is all in retrospect. At the time this game was made, that second game probably wasn't out, so none of this would mean anything. But I mean, it's still really cool in hindsight. I can look back at this game and what it set up, right? :P