Delta Chat doesn’t have their own servers but uses the most massive and diverse open messaging system ever: the existing e-mail server network.
Email uses an indirect federated network, meaning the communication passes through a number of servers. This design isn't secure on its own as any server point on that connection can be corrupt, as in tampered or spoofed. That's unless the whole communication is encrypted and/or tunneled from multiple prying servers/connection points.
XMPP uses a direct federated network. There's only two or 1 servers on this kind of network (there can be only 2 more connection points if a BOSH or Websockets proxy is used). The servers have to be known as trusted, and the clients can't spoof to their host server, unless the device (such as a user's phone) is physically stolen or a password is stolen. Provided the two servers are trustworthy, these two servers make a direct connection, preventing sources of spoofing or tampering between them.
A direct federated network makes direct connections: from client, to server, to server, to client. If Bosh or Webproxy is used, it goes: a connection manager is added between a server and client on one or both ends. Sometimes the servers are the same, and the connection manager is usually on the same physical location as the server. There's some data that only the servers can write to, or overwrite for sending, so that the client can't spoof it to the other end.
An indirect federated network has something like that, plus a lot of other pass through connections, which is what email is. Delta chat may be good as an alternate way of messaging, but using the same system means it uses an indirect federated network, unless there's a difference in implementation.