The hotel agent probably has a RAG that points at their various customer and inventory databases. The user agent has individualized information about the customer. Both of them have also likely had SFT steps that further differentiate them.
The interesting question is if Gibber-Link lets the AIs do something they couldn't otherwise do with natural languages. Does it lower some error rate? Does it reduce the time it takes to send messages? Does it effectively give the AIs additional vocabulary?
If I had to guess at the internals, they probably took the token encodings and mapped them on to tones. Then it just throws text or audio through the decoding filter and passes it back.
If that's the case, the benefits are probably limited to slightly faster communications (It's essentially a simple, lossless compression) and a slightly lower error rate (beeps are easier to correct in noisy environments).