Full control over the Intel backdoor / remote administration engine that's on all their modern CPUs. (It may not be an intentional backdoor, but it's certainly looking as if it's been usable as one by intelligence agencies.)
Edit: I read some more. It looks like this is going beyond what I thought and affects way more machines.
That PDF also says your BIOS must support this kind of debugging, and, for the ‘OOB’ protocol, your hardware must support it. So, your BIOS may be configurable to make this attack impossible, and your hardware may already be protected against it.
[1] https://security-center.intel.com/advisory.aspx?intelid=INTE...
https://security-center.intel.com/advisory.aspx?intelid=INTE...