The idea itself is sound: if there are no SGX bypasses (hardware keys dumped, enclaves violated, CPU bugs exploited, etc.), and the SGX code is sound (doesn't leak the private keys by writing them to any non-confidential storage, isn't vulnerable to timing-based attacks, etc.), and you get a valid, up-to-date attestation containing the public key that you're encrypting your traffic with plus a hash of a trustworthy version of the SGX code, then you can trust that your traffic is indeed being decrypted inside an SGX enclave which has exclusive access to the private key.
Obviously, that's a lot of conditions. Happily, you can largely verify those conditions given what's provided here; you can check that the attestation points to a CPU and configuration new enough to not have any (known) SGX breaks; you can check that the SGX code is sound and builds to the provided hash (exercise left to the reader); and you can check the attestation itself as it is signed with hardware keys that chain up to an Intel root-of-trust.
However! An SGX enclave cannot interface with the system beyond simple shared memory input/output. In particular, an SGX enclave is not (and cannot be) responsible for socket communication; that must be handled by an OS that lies outside the SGX TCB (Trusted Computing Base). For typical SGX use-cases, this is OK; the data is what is secret, and the socket destinations are not.
For a VPN, this is not true! The OS can happily log anything it wants! There's nothing stopping it from logging all the data going into and out of the SGX enclave and performing traffic correlation. Even with traffic mixing, there's nothing stopping the operators from sticking a single user onto their own, dedicated SGX enclave which is closely monitored; traffic mixing means nothing if its just a single user's traffic being mixed.
So, while the use of SGX here is a nice nod to privacy, at the end of the day, you still have to decide whether to trust the operators, and you still cannot verify in an end-to-end way whether the service is truly private.