The same way it works everywhere else. The bank sends that information to the program. (That's also how an airline knows you've got a credit card that gives you benefits like a free checked bag or priority boarding. And/or, at, AA, a similar rebate on redeemed miles, though capped at AA while it's uncapped at IHG.)

Come on, for one thing, they'd know because you're earning points with the card and/or earning annual free night certs with the card! So how could they not know you've had the card?

So the only question should be about timing: If you get the card, how soon do they know you have it, and if you close the card, how soon do they know you no longer have it? (And I don't know the answers to those.)

But factoring out the timing details, it's obvious to IHG you have the Chase card if points from the card and/or certs from the card are posting at least annually.

(For all I know, Chase may even send the statement points total to IHG every month, even if it's 0. But they certainly send it when it's non-zero.)

By the way, in case you forgot, another benefit of the Chase card is that it gives you Platinum status. Obviously IHG has to know you have the Chase card to do that!!!