I think you have a couple of different issues there. One is any disability (or even depression) that he may have. He may actually be trying to do what he should be doing, but if he has some disability or depression that makes it difficult for him to do what he should be doing; there's not much he can do about. With regard to helping a person with a disability or depression, I pretty much think most parents ought to do what they can to try to help their kid get on his feet. (He's only 23. Even a healthy 23-year-old can have trouble getting on his feet these days.)
I think helping him is his mother's and father's job, though. I don't think it's really right for anyone to expect you to kick in on helping him. He's not your kid. Understanding that your wife would want to help him is another thing.
If he has no way to get to work without transportation, maybe it's reasonable for his father to hope you'll let him use it (if you're not using it). If you bought it, though, and if the deal was that he'd pay you for it; nobody could blame you for wanting to sell it. If he's going to use it for getting to work I think you should expect him to start paying for it out of each paycheck (even if it's a small but regular payment). If he's already getting himself to work (when he goes) or isn't going to use the thing to get to work, then I think you ought tell him he can start kicking in some money or you'll need to sell it.
If he's got something like depression, his parents could tell him he needs to get professional help. Maybe if he's get that and sticks with it, you'd feel better about giving him a little more time with the motorcycle.. There's not a simple answer if a kid (and he IS still a kid) has some disability or problem like depression.