Most of the Huawei Mate 9 parts are made of metal, except the top and bottom parts, which are made of plastic to allow a signal through. Even the sides of the phone, the earpiece and buttons are all made of metal. The Mate 9 also comes with a two screws at the bottom of the phone that fasten the rear panel with the front frame together, thus improving the durability of the phone from and protects it from breaking when it's being bent.
I've read in several places that some websites mentioned an all-metal body, but apparently it's isn't the case. I base that based on this video by JerryRigEverything that put the Mate 9 to an intensive durability test and he mentioned in his video that the top and bottom parts are made of plastic, not metal; here is the video.
The back brushed metal frame gives the phone it's premium look an feel. As you can see in the video above, the aluminum back get scratched, so don't confuse of metal build to scratch-resistant. I personally would still use a cover to protect the phone from scratches. Also, as you can see in the video above, the Mate 9 has very good build quality, it's not get easily bent.