At the center of at:// is a question of identity.
For identity, you want some kind of a global login, or a "handle", that you can remember. at:// uses domains for that (e.g. my "handle" is danabra.mov). That is literally DNS.
However, you also want somebody to hold your data. Most people don't want to host their own data. (I don't.) So that's where the notion of hosting comes into play. My current host, as explained in the article, is https://morel.us-east.host.bsky.network. (That's also resolved through DNS.)
Finally, the important bit is that I (as an identity) should be able to change both my handle (i.e. how people refer to me) and my hosting (i.e. where my data is stored) without breaking any links to my data from other data ("links between JSON" is how we represent "reply to a post", "like to a reply", "follow of a person", etc). This is why links are tied to an identity rather than to hosting or to handle. The identity document also contains my public key which is important to allow trustless caching and retransmission of the data.
That's about it.
>But from a technical POV, I'm just not seeing why I'd want to use this instead of reviving those older but proven technologies.
I think everything being signed is a big one. There is no need to trust anyone retransmitting the data because it's transferring signed commits. But yes, this is essentially a fusion of something like Git with something like RSS, but for JSON and on top of DNS, HTTPS, CBOR, and WebSocket.
Compared to RSS, the novel parts is that you don't need to trust the retransmitters, that it's pushed via WebSockets, that it scales to real-time communication for millions of users (in production today), and that it's application-agnostic but the data formats are application-controlled. E.g. we have different apps like Tangled.org (GitHub on atproto), Leaflet.pub (Medium on atproto), etc, all able to "see" each other's data and interop.