Well I'm diagnosed with social anxiety disorder and am on the autistic spectrum, so...
I also experience intermittent clinical depression, associated with said social anxiety. In layman's terms, I get profoundly lonely.
In my experience (anecdotal though it is,) there's no correlation between passionate fandoms and mental illness. But what's important to remember is that mental illness can affect anyone, at any time, and is ultimately just an illness like any other. The reason it garners such a stigma or a particular kind of attention compared to physical disease, is simply because our minds are where our sense of identity and personhood live. So when that becomes somehow perceived as "defective" people feel it's somehow far worse than a physical ailment.
In reality though, is IS a physical ailment. The brain was a physical organ (or group of organs) last time I checked.
And like any physical ailment, people respond differently to different treatment regimens, some make full recoveries, and others struggle with them chronically all their lives.
As it pertains to Shenmue though... I'm sure my autistic side probably does make the minutia and detail oriented worlds of the games a little more attractive to me than they might otherwise be. :p But I'm also sure there are far more people who love them who aren't in that boat.