The Diners Club card is a pure chip and pin card as far as I can tell. The documentation says I have to use the PIN, no mention of using a signature.

It's issued in the USA today. The fact that the card is not accepting new applicants doesn't change that. The card is being issued to existing holders of a Diners Club card account. And although the bank has a Canadian name (Bank of Montreal), it also operates in the USA (whether on its own or through its Harris Bank subsidiary).

(However, you were technically correct, simply because the Diners Club card is a charge card, not a credit card.)