I believe that's the correct PTO, don't think there's any difference for the uses. There is different PTO's for narrow frame vs. wide frame.
I would suggest going to the CC parts look up to compare what you have vs what it shows. The arm that disengaged the PTO has a "button" on it, can be made of different materials, I believe the first were fiber.
Yes, that's in need of rebuilding, the center button is missing.
There's several parts sources available for the PTO. I haven't rebuilt one in 10+ years, so I'm not up to speed on prices. Cub Cadet Specialties is probably the most complete and popular supplier.
There's plenty of "how to's" easily found and it's good to familiarize with the procedure before you jump in. One frustration is removing the set screws, two in each hole, 3 holes to remove the PTO.
Nothing overly complicated, just take your time and enjoy the process!
Best of luck,
David