So the rook checks. And, because the rook covers all the possible escape squares, the black king is in checkmate. The position below is a checkmate position. However, just because the rook checks does not mean the rook checkmates. The piece that moves, and, due to its action, results in an enemy king being in checkmate, is the piece that causes the enemy king to be checkmated, through its action. That piece is the king.
You're losing this argument for the simple reason that you're providing invalid, terribly-thought-out "evidence".
And as the rules dictates, it's the piece that checks (attacks) that checkmates. The white king is not attacking. The white king is not attacking the square the black king occupies, is it? Either it is or it isn't. If it isn't, then it's not checkmating. Again, the rules only define the checkmate position, NO mention is made of how that position came to exist so no consideration is given to the previous move.
This is easy to verify. You claim the action of the last move results in checkmate. Where in the rules does it say that? It doesn't. BUT, it does say the action of the attack on the enemy kings square (in this case the rook) results in checkmate.
See how that works? Your claim is nowhere to be found in the rules, it's your own interpretation. My claim is found in the rules, in black in white. No interpretation needed.
Imagine that you're in a room with an activated death laser pointing at you, blocked by a rock. If the rock moved, would an observer say that the rock killed you? Or was it the laser?
the rock, because the rock moving resulted in my death
But it was the laser that killed you, correct?
At this point I think he is just trolling.
If anyone here is trolling, it's you.
Except you are smart. You know the answer. You even admitted in one of the diagrams it was the rook that checks. So you know. I know you know.