Poor baby. His missing leg looks so painful. If I had to guess, I would say it was an injury, possibly if it was in the same shape as the remaining leg. It's pretty swollen.
That being said, the other leg doesn't look good either.
I would give it a few days. You'll probably be able to get a feel for his quality of life. If he's eating well, being a little fighter, you can always see what you can do. There's plenty of stories about one legged chickens, but I haven't seen any with the severity of the deformity of the other limb. It could have a slipped tendon, but there's likely not anything you can do about it if that's the case.
You can make him a little chick chair with a hole in the bottom and dangle his leg through the bottom, just to see if you can get him to stand on it and build muscle in the leg.
One thing you might be able to do, although it sounds crazy, is build him another leg. Bear with me. If his missing leg is healed and not sore to the touch- you should know if it hurts if you touch him- there's a good bit of it left. If you could build some little contraption like a splint, with wooden sticks that go around the leg and connect to a "foot", maybe some cardboard that he can try to balance on, it's worth a shot. I've never done it before, I'm just spitting out random ideas here.
Another random idea... a cart. If you could build it something out of a toy car or something with wheels that would stabilize it and allow it to scoot around with the good leg, but would help it to keep going.
I read about a turkey who lost their leg at an early age. The owner put clear aquarium tubing over the end of the joint and cut it to the correct length of the other foot. It had to be replaced every week or so, as it fell off a lot (it was loose so it didn't hurt) and the turkey grew.
I think that it's not necessary to cull right now. There are lots of options to try if you're willing to try them. I know how hard it can be to make the call. If you exhaust them all and baby is still in pain, you know what to do. Otherwise, I think there is a chance for baby to live a semi-normal life, but the sideways leg can throw a kink in the plans.
Here's a thread from 2010 about a similar dilemma, although this chicken had one normal leg.
https://www.backyardchickens.com/threads/chick-hatched-with-one-leg-any-hope.397026/page-2
Keep us updated. Hope this helped generate some ideas!