While I believe the only Black and White world is on the chess board, I couldn't answer the poll with 99.9997%. While this discussion is dangerously close to "How many angels can play the same harmonica?" and what exactly is YOUR definition of "playing harmonica", let me tell you a story about two kings.
A wise White king tells his armies to move out into threatening positions developing slowly and not over extending himself or his pieces. His impatient enemy the Black king is threatened and confused by the flury of attacks and so engages them disjointly. The Black king can't remove them all at once and so must respect them all and is thus backed into a corner and pinned down. The White kings sees the openings and puts the Black king in repeated Check. The end is inevitable.
It is possible to win (although rare) at chess without ever taking one of the opponents pieces. Only against fools can one win without ever threatening a piece. For me, winning at chess usually means threatening my opponents pieces, area of the board and ability to move. Most often the THREAT to those things is more powerful than the reality of TAKING them. While one seeks Check-Mate to end the game, the condition of Check FORCES a proper, logical response from the opponent. Chess is not about killing pieces; it is about taking away the others ability to wage war.