I llike the game examples, to me they are really inspiring in terms of defining what BSG is.
Unfortunately unaware of Wilmot's Warehouse. What about Rodent's Revenge - I feel like those shouldn't be BSG.
Games like Go, Gomoku, Connect-4, Sokoban, are not BSGs, according to me :D .
Match-3
I think BSG is closely related to Match-3. I'd assume there is quite a significant overlap in the player-base that enjoys both genres.
- Bejeweled, Candy Crush, Zuma, Luxor are just match-3 and not BSG
- Puzzle Bobble / Bust-a-Move style games ...?
- Puyo, Dr. Mario, Vertrix combines the mechanics of BSG and match-3
- Panel Attack, Pokemon Puzzle Challenge - I always thought they are BSG but are they just match-3?
- Mr. Driller, some games where you click connected tiles with minimum size to remove them (titles?) - shares the gravity mechanic in some Tetris games so it feels a little bit BSG-ish.
Tetris
My initial perspective is that BSG is a very, very specific game type related to Tetris. Sure BSG doesn't have the word Tetris literally in it but it came from the Tetris community (I presume) and has a specific player-base. Just like in rogue-like games you don't have to be a rogue, the definition doesn't come literally from the words but also from social / historical reasons.
From that perspective, maybe games like Puyo Puyo, Dr. Mario are even only borderline BSG. The Tetris vs Puyo game brought the two together.