The glasses that Kirk gives to the dealer *won't* eventually become the ones he gets in the future. Indeed, they can't be, because with enough trips around the time loop, they'd eventually crumble away to dust.
They don't age more through an extra loops. They only age the time it takes to go from TVH to TWOK (300 years). They aren't infinitely repeating the same events, it's just the effect preceding the cause. It's a paradox, but that's it. The glasses could be sold by Kirk, bought by McCoy, given to Kirk who sells them back to the same store McCoy sells it to. It might not follow linear logic, but it's fine for time travel logic.
It's just a joke, though, so nobody should overthink it (if you do, conclude that the Vulcan Science Directorate is correct).