Hyperchains are strictly based on the existing Aeternity implementation - by launching your own hyperchain you instantly gain access to all existing features of the AE ecosystem - FATE VM, Sophia, Oracles, Smart Contracts, State Channels, Naming System, etc…
Previously you could do it but the security would be questionable as for your private network to be considered safe you would need to create an immense decentralized network of miners. Hyperchains provide you instant maturity and security of your network even with very limited resources.
The hyperchains concept could be applied to other networks as well but for now Aeternity is creating the first implementation based on the Aeternity node.