I mean, technically i implemented it with a few different board states to help organize the 'common knowledge' board, the 'up-to-date' board, and each players' respective information. :)
Beyond that, what you described is basically how the implementation operates anyways. it notifies a player if they are put in check (without identifying the threatening piece, though I could change that pretty easily), likewise if theres a checkmate/stalemate. And in a situation where only one move is possible, it just auto-uses that move and notifies the player.
So the two players dont really 'discover' the outcome of the game out-of sync, per se.
An especially fun part is related to piece capture - eg if black captures white's pawn, then on white's turn, they will simply see their piece missing. So technically they would 'know' about the capture before their opponent would, which...I cant really even imagine the implications of yet, since I haven't had a chance to playtest this variant yet :)