Great photos! I think from the label it looks like some model from Panaracer. If it's a "Tourguard" version, the ply you see under the tread is the anti-puncture Kevlar belt. (Maybe that's why it's lasted so long?!?)

If it's a "Tourguard" version of any Panaracer model, I'd think that tire could go another... 500 miles? 1000? Good thing it's on the rear: a flat there is much easier to control than on the front.

When you take it off, it would be interesting to cut it open to see the belt laminated under the tread! I've used scissors in the past, but I'm not sure how easily they'll cut through Panaracer's Kevlar.