the rarest checkmate, the doubly disambiguated bishop capture checkmate

For anyone wondering, this played in about 1 in 342 billion games.
This statistic doesn't really mean anything. In most of the games this is played, one or both players are just playing to make this move, not to win. It's essentially so rare that it would virtually never occur in a game played by computers (I would think less often that 1 in 342 billion games), but is easy to make in a game against an opponent moving randomly.

With a doubly disambiguated bishop move, you’re not attacking any new squares, so it would have to be a revealed checkmate.
Furthermore, because of how the bishops have to be arranged, a vertical revealed checkmate is impossible, so it had to reveal a checkmate by a 4th bishop of the same color, or a queen.
I'm not sure I understand what you're saying here. How can a bishop reveal a check by another bishop of the same colour? And why can't it reveal a discovered checkmate by a rook? Here is an example of a game I played against Martin - it's a capture checkmate, but a discovered rook checkmate nonetheless:
104. B1xb2 Kh2
105. Bc1 Kh3
106. Rh4+ Kg3
107. Bc3b2# (doubly disambiguated bishop non-capture checkmate)