Surely overall responsibility for delivering a product to the customer is the owner of that product. If they farm it out to an agency they can not relinquish final responsibility. Consider all the contract pilots who fly for RYR. It is RYR who control directly the quality of how those pilots operate and the number the agency provides. Same here. It is RYR's responsibility to ensure that its agents have the tools to do the job. Howvere, if RYR only pay them enough to open too few desks they have not been given the resources to do the job. Swissport can only provide the resources they have been paid for. Hence RYR's campaign to eliminate check-in desls and hold baggage; cost saving.
Question still remains; you turn up at the instructed time; are not able to check-in due lack of staff; miss your flight; who do you claim against and what is your compensation. Seems like it would be no different, at least, to being bumped off due over-booking.