the protocol is very generic and does not require anything related to phones. it is actually 3 parts, a key exchange, a signature mode and a ratchet. how you combine these is up to you. the app is one way to combine them with phones. there's other ways to use the protocol, that could also be applied to emails
There's no reason why the Signal app couldn't allow you to register mailto:joe@example.invalid as well as tel:+18005551212; it just, currently, doesn't.
And of course the protocol in general is much higher-level than that.