eh, it runs on e-mail infrastructure; also, it does a little bit more than messaging.
You can use your usual e-mail ID, and message anybody else's e-mail ID, but securely only if they also use Delta Chat. To work around the big servers seeing your social graph, they recommend using randomly-generated IDs on always-encrypted tuned e-mail servers that they call "chat mail" servers.
Either way, you also get user-to-user web apps called WebXDC. This is something even some XMPP clients have added nowadays.