Yes it's a v1.6 Xbox console.
You'll need to find an Xbox PSU specifically for a v1.6 console and match your input AC power specs. (e.g., 120VAC or 220VAC).
Looks like IC21 blew out and blew the top off that capacitor with it.
The Xbox Repair Guide isn't going to help you for component-level repair of a V1.6 Xbox Power Supply Unit (PSU).
ebay, craigslist, offerup etc are you best bet to purchase an entire used 1.6 console for spare parts. Years ago, there were a few 3rd party vendors that made replacement power supplies for the Xbox console; however, they've been out of production for many years.