A cryptographic identity is a public key as used in a public key signature scheme. So a particular person is represented by a ridiculously long number. That number can be shortened with some sort of hash to a shorter value to make a key fingerprint, which is a shorter ridiculously long number.

The scheme described in the system seems to use a blockchain to create a shared mapping between a name and a cryptographic identity. So a third party is still in control of that mapping, but there are a lot of third parties and most of them would have to conspire to forge a mapping. Then you could send a message to a name, rather than a number, with confidence that someone in the past picked that name and locked in the mapping between that name and the cryptographic identity.

The append-only, distributed nature of the traditional SKS PGP keyserver network seems to provide the same sort of thing. If you query several keyservers you can be reasonably sure that someone mapped a name (and email address) to a particular cryptographic identity sometime in the past. A single server operator can not forge a mapping without the possibility of that forgery being detected.

The thing is, people don't actually want a reliable name to cryptographic identity mapping service for end to end encrypted messaging. They instead want to be sure that they are securely exchanging messages with an particular flesh and blood person, and if you want to insure that you are back in the realm of ridiculously long numbers.