I think you're right.
Most scholarly stuff uses 'Turkic' to indicate the central Asian people distinguished from more recent 'Turks'. Was it just ignorance, or was the author trying to convey some PC idea?
It isn't precisely clear if the DNA indicates ancient Anatolians or ancient Turkic peoples.
Isn't there some thought that the ancient Egyptians came from farther WEST, driven into the Nile valley by the drying out of the once-fertile area now the Sahara?
The initiators and first bosses of the Egyptian civilization were probably Sumerians. The population may well have migrated east as you suggest.