It's an AE construction, but not necessarily an AEAD construction. You can have IND-CCA3 security without additional data.
The converse is also not necessarily true (i.e. an AEAD scheme could be based on MAC-then-Encrypt and IIRC there are some that are built that way), but that's a less useful counterpoint. The recommended AEAD constructions (AES-GCM and ChaCha20-Poly1305) are EtM.
