thought game: check redefinition

Let us redefine a check in the following manner:

A king is checked by the figure iff this figure can capture the king in the next move.

This seems pretty innocent, but gets funny when we are dealing with forked figures. For instance, if we have a black King on A1, black Rook on B2, white King on C2 and white Bishop on, let us say, G7, black to move:

1. the white King is not in check, since the Rook is forked

2. Black has two legal moves: Ka2 and Kb1 (sic!). Curiously, both of them are checks:
2a. if Black plays Ka2, the rook is no longer forked, therefore it MAY capture the white king
2b. Black may play Kb1 because this field is protected by the Rook, which also won't be forked anymkore. Now, both the King and the Rook check white King.
3. In both variants, Kxb2 is a checkmate.

What do you think of the idea? Can you come up with any funny puzzles for this variant?

Your idea doesn't work. There is no rule that restricts the rook from capturing the king. It doesn't matter if the black King will be captured in the next move. That's not how chess works. The winner in chess is the one who captures the opposite King first. So in this case black would simply capture the white King and win.
What you are trying to say is what if we change the rules so that in order to win you must not only capture your opponent's King but your King should also not be captured in the following move.

@Zapala are you a logician?
if not, dont ever try to be one :)
just kidding but your definition of check leads to.....
(drums)
normal chess!

@MorningCoffee

Not really. In chess me and (as it would seem) quite a lot of people on Lichess are playing, a move that would put your own king in check is forbidden. Therefore, in a situation described in the original post, while in normal chess there would be a check from the rook, the rook cannot play Rxb2: it is pinned. So, in proposed variant, there is no check.

If this variant is normal for You, I would love to see some of Your endgames.

BTW: while ring theory is definitely my main field of interest, my knowledge of formal logic seems to be just about sufficient for Internet arguments

@zapala
look im not into explaining in detail why a conclusion is illogical because when people dont spot their own mistakes after being told there is absolutely zero chance I can convince you
if you think your premise "A king is checked by the figure iff this figure can capture the king in the next move" leads to a different kind of chess, then...
good luck to your ring theory adventure, I m sure galois will be shaking in his grave. Just dont consummate the field, leave a theorem or two for some other poor guy to discover.

By your definition, the white king is in check, since the bishop doesn't threaten to take the black king. (he can't play Bxa1 after Rxc2, since he has already lost the game)