This is definitely interesting (and probably the first end-user-valuable SGX-on-server application I've seen), but there are two issues IMO:
1) Intel SGX isn't really capable of resisting moderately serious physical side channel attacks by someone with physical proximity or access to the server. It's decent for low-value, or widely deployed apps where compromise of a single instance only hurts once user, but for a central singular service, less so. Inferior to, say, a conventional HSM with code run inside it. (SGX would be great for client-side stuff, or for, say, a Tor or multi-server VPN server array, which is something I worked on using TXT before.)
2) Intel's still a gatekeeper on what SGX applications can be meaningfully distributed; to run in release-mode, you need a key signed by them, and to get this requires a commercial agreement. If you run in debug or pre-release, anyone with a debugger can pull keys.
If Intel were to fix the latter (even if it cost, say, $100 to get the signing rights, or some non-discriminatory "you must do X, Y and not A, B" were published), the former wouldn't be a deal-killer for some things. If the server operator were a mostly-trusted third party (e.g. a cloud provider), and the people writing and signing the code were never able to get physical access to the hardware, it might work a lot better in most server threat models.
In Signal's particular case it's probably true that most Signal users trust Moxie/OWS, and this is really about putting a much higher bar in place for government compulsion to tamper with or disclose the contact info, so this is a net win.