That's just a normal CR2032, but unfortunately one of the times they soldered/welded wires to it and shrink wrapped it, instead of just using the normal battery holder. It's not rechargeable. There are replacements for this annoying variant of the CR2032, but far more difficult to come by than the standard battery which you can pick up with your groceries. You could try ASUS support to see if they can sell you a replacement, or try Ebay or Amazon.
N.B. The polarity matters, ensure that any replacement is wired the same way (positive & negative). This is also a problem that doesn't really exist with a normal battery holder.