How would Chimera Shadow play or how what would he consider to be fun for him to do?
Challenging Sonic. I guess some things never change lol!
But it's much less of a "I got to prove I'm better" kinda way... And more of because he loves the challenge in itself. They are still rivals in a way but it's a very friendly kind of rivalry considering the two are much closer in this AU compared to canon! Chimera Shadow may have a billion different abilities, Animal, Doom, and Chaos. But Sonic has determination and is able to take him on despite everything. It's something he admires about Sonic!
He also likes to chill around a lot. When there's no danger happening he sometimes likes to sacrifice some of his energy to fly around with his Doom Wings, soaring through the clouds to feel free. Something he wasn't able to feel for a long time until he finally let go. He also likes to stargaze a lot too!
He also likes doing casual things with those he considers his "found family". It's the little things that mean everything to him. Playing board games, watching movies, visiting places, listening to his friends' fixations, getting his nails painted with Rouge, etc etc. just being in the presence of those he loves is enough for him.
Shadow may be very nonchalant and blunt, but he's very genuine and sincere in every since of the word! He even inherited some of Maria's interests.
Another thing he loves is animals! He loves to pet and care for them! I guess it makes him feel less like an oddity and makes him feel connected to his roots if that makes sense lol! (He really likes snails for some reason).
That feeling of being the only one of his kind is probably also one of the many reasons why he adopted Eclipse.
TLDR; Shadow lives for the small moments while Sonic lives for the thrill of adventure