‘63 Valiant - steering shaft play

Here's the statement about the kit on their website: "Steering Column Knuckle Kit All Makes. Technically for the 1967 and newer columns, but we have used them for earlier cars with no issues or problems. 63 -79 - All Mopar -"

I'm guessing the shoes are shot, so if those parts fit I think I'll be OK.
At the very least, be sure to take it apart to see what's going on before you buy anything. There are several versions of these couplers and they're all slightly different.

You may be able to use the shoes in that kit, but you won't be able to use the seal, seal retainer, or spring. Hopefully your spring isn't broken.