I think it's easy to get carried away when we think about tires.
There's a pretty easy way to tell whether the tire's integrity has been compromised or not. Tires are made of rubber that encases nylon, kevlar, and steel cords, giving the tires their strength. Any kind of a gash or tear that doesn't expose the cords is perfectly safe. You can run the tire forever and it won't suffer any negative effects because the structural cords aren't impacted. But if the cords are exposed or damaged, the tire must be replaced.
The OP's tire doesn't appear to be showing any cords, so it's perfectly safe. It's not a close call, and replacing the tire would only make his wallet lighter.