* A set of software tools: Check
* Unauthorized user: Check Caveat: user is not authorized by you, but by someone else (Intel)
* Gain control of a computer system without being detected. Can access your machine while it appears to be "powered off" but plugged in. Has full access to RAM. Can draw undetected on top of screen. Can read screen. Check.
So. Does this qualify the Management Engine as a rootkit? It meets the definition. Just because the rootkit is installed by the manufacturer doesn't make it less of one.