Cryptocurrencies don't necessarily have to be mined. Some newer ones have systems that aren't computationally intensive; they do that by effectively inverting the system of responsibility: they work by saying "if you hold our token, you have a vested interest in the integrity of the chain, therefore we trust you to validate transactions for the network" where "validate" means "vote on whether a transaction is legitimate".
It's fairly interesting and still under research but on some smaller cryptocurrencies it seems to be working. Google "proof of stake" for more.
edit: for a single organization that might not be very useful, as you already have one big central entity that you trust (the organization itself) but it is potentially an additional layer of security that can be tailored to the organization's needs.
