I like the vibe of this as you travel further north the stranger and weirder things get and I like the hook you built in with the game of champions to have players use and find pieces in the world to honorably get the Prince back.
There are a few things I would suggest. You noted for one of the characters how you would obtain their chess piece. I’d like to know what deal is required with the others? I know we players love our murder hoboing but seems like there is opportunity to say do a small task or quest for the lake lady or help the head on the hill track down Fodoc. Little mini quests to earn the pieces as I suspect most players will not put any weight into the chess pieces so unless they get the one at north winds cave and then hit the right random encounters, slaying those beings, and just picking up the chess pieces by happenstance, they will arrive at the giants hall and turn around to go find pieces in the world before returning. Not that that’s bad but “the holders” of these pieces probably need something to relinquish the pieces in question.
Also while it’s a point crawl I didn’t see any info on distances to determine travel times unless I missed it. With the brutal winter weather knowing your distance of travel will help you determine how much gear you’re packing to get to your next destination and it will make your winter weather system effective in instilling a certain player/PC reverence for the elements.