So what happened was that they didn't replace the card on file when you checked in.
Upon check-in, we provided our personal credit card for room charges and incidentals, which the front desk swiped into the system.
When I check in it usually goes something like this:
(front desk): Can I see the credit card?
(me): Sure.
2 possible scenarios: front desk takes a look, confirms the last 4 or whatever visually and that's it, or they ask me to swipe it.
I've had the front desk say the card is for incidentals the vast majority of the time (maybe all?), and the only time they mention about the room charge is if the card I presented is different. Then mostly they will ask if I have the other card, and if I don't will say they have to charge this card. Sometimes they ask which card the room charges should go to. And sometimes they say nothing, and you find both cards get billed (or in your case the card that wasn't swiped).
People who work in hotels can chime in but I think most often it is a front desk checkin issue, though the night auditor or the person doing the checkout may have something to do with which card gets charged as well (I think one time I got asked during my stay, as they were confused. It was a long stay so they were charging running a charge before I checked out).