From what I can tell it appears to be a replacement FCM/APNS. The client subscribes directly via websocket to a self-hosted server (Go binary).
New messages in the queue are then notified (gotified) via the websocket. https://gotify.net/api-docs#/message/streamMessages
The payload can be picked up and managed via REST API as well.
I'm building a similar solution for a slightly different usecase, so wanted to have a look under the hood. There's nothing I can see that would stop you using this for iOS so maybe they just don't have a iOS dev on the project.
Edit: Ah, here's why. https://github.com/gotify/server/issues/87