Indeed, this ring is called "Immobilizer transponder ring".
Here's what one website says about it: "Transponder keys emit a special signal to the ignition to let it know that the right key is in the lock. The signal receiver in the ignition is known as an immobilizer."
From now I personally would be cautious replacing this thing. If it acts as a "mean" (which is most likely) by which the signal is sent/received then it's ok. It just reads the code from the transponder located in the key and sends it further to the immobilizer. That's why you have a wire - it connects to the immobilizer.
What I would do is disconnected the battery, replace this ring and try to start the car. In the worst case it can show you "Start Error" on the dash board". Then disconnect the battery and replace it with the old one.
Let me give you an example. I had an ignition lock fully changed couple months ago and tried to start the car with the key provided with the lock. (Apparently this key is used to configure the lock pins and not for starting the car, since it doesn't have any transponder). The car didn't start and I saw "Start Error" on the dashboard where mileage is. I simply disconnected the battery, removed the key, reconnected it and normally started it with my OEM key fob.
Hope I gave you the overall idea. That's how understand it, and I think it shouldn't be a problem when replacing it since this part acts as "Intermediary" between the transponder in your key fob and the immobilizer.