Haha
Please take my rook!

Of course, he needed to be sure I took the rook with my king or pawn and not with my rook or knight. Either of those would unlock his king.

So I also discovered the "mad rook" concept. I'd say that puts me in good company!

Wouldn't work.
If he doesn't check White can simply play Rf3 (or RxR if available).
If he does check White can play Ke3 then move the knight (possibly blocking check or capturing).
If he doesn't check, Rg4++. If he does check, blocking with my knight was plan B. Plan A was to pray he didn't see the possible stalemate.
Wouldn't work.
If he doesn't check White can simply play Rf3 (or RxR if available).
If he does check White can play Ke3 then move the knight (possibly blocking check or capturing).
If 1...Rd4+ 2.Ke3 Rxe4+ then 3.Kf2 (missed that out in the version you quote).
As you so rightly point out - if he doesn't check he's mated. (Missed that too.)

So I also discovered the "mad rook" concept. I'd say that puts me in good company!
You mean, that puts ME in good company! (no me, no me...)
OK, you win. I agree....it puts YOU in good company.

However, the knight could easily block one of the rook checks, making this position a win for white.

However, the knight could easily block one of the rook checks, making this position a win for white.
Yes....that was my fallback plan if he went for the stalemate. But he didn't, and he gave me the opportunity for the Rg4 checkmate two moves later.
As we got near the end of this game, he could not move his king, and consequently, if I take his rook, the game is a stalemate. I wondered how this would play out....him trying to make me take the rook and me resisting. Weird. However, he evidently didn't see it and allowed the checkmate. (It's black's move here.)
Black is doomed. White is up material
However, the knight could easily block one of the rook checks, making this position a win for white.
Yes....that was my fallback plan if he went for the stalemate. But he didn't, and he gave me the opportunity for the Rg4 checkmate two moves later.
Yes
1 ... Rd4+ 2 Nd3 (the king has an escape square)
1 ... Rb2+ 2 Ke3 and 2 ... Rb3+ 3 Nd3 or 2 ... Re2+ 3 Nxe2
As we got near the end of this game, he could not move his king, and consequently, if I take his rook, the game is a stalemate. I wondered how this would play out....him trying to make me take the rook and me resisting. Weird. However, he evidently didn't see it and allowed the checkmate. (It's black's move here.)