That explanation of Kinmune = Eye could work, though I feel it needs some refining.
I have trouble seeing it. Kinmune was trapped deep under Sarthaal, in the Dwemer ruins under the city. The Eye of Magnus being found in Sarthaal seems to be a bit of a tenuous connection, particularly since it's not (I don't think) in the Dwemer ruins. She was active the whole time too, learning magic from the sounds of the steam machines. She then broke free, and went for Tiber Septim upon detecting his thu'um.
The text also mentions that her being transported to the past "drove her insane", and later became "one of the Arena’s most feared villains". I'd like to say Kinmune is the Underking. Both of them, perhaps. Her connection with Tiber Septim is apparent, and insanity is a typical trait of Akatosh. Both Tiber Septim and Zurin Arctus further this connection with Lorkhan and Akaotsh, through the enatiomorph (sp?). The Underking was also one of Tamriel's big bad guys in his day, wasn't he?
Granted, I've no idea to what 'tenth anniversary remembrance of the Insult of some wrong-headed cave-totems' refers
Tenth anniversary of 9/11, I'd wager.