You asked a few questions,
My question is, how would employers view a character reference received from someone whose relationship with the candidate extends only as far as online interaction through gaming?
Ultimately, that's on your friend, not you, to decide. There may even be specific reasons why he's picking you (maybe he's applying for a job developing games?)
It may help to understand the context of what he's asking for. Interviewers will generally be concerned about many aspects of a candidate's fitness: their technical or job skills, their soft skills - communication, teamwork, and so on, and their character or culture in terms of fitting well with the employer.
Ultimately, a character reference is one of many tools an employer will use to evaluate the candidate. Each tool used will have a purpose - and, as may be obvious, a character reference is meant to evaluate character, personality, and soft skills - things that are inherent to an individual and not specifically to their employment history. In other words, although you do not know the person in a workplace context, you do know them in a context that lets you comment on their soft skills and how well they work in a team environment.
So, let's get back to the rest of your questions:
Should I be frank about the nature of our relationship or should I skirt around it in more generic language?
You should be honest and concise. You don't need to hide anything but you don't need to be detailed, because the interviewers probably don't care if you're part of a gaming clan together or any other similar social construct - maybe you're on the same community softball team or whatever. It's fine to mention that you've worked with him as leaders of a hobby club or a gaming team or whatever language you find appropriate.
Do I defend it and explain why I think my appraisal of his character is meaningful or do I just own it and pretend as if it's the most natural thing (which really, it is)?
No, don't defend or explain anything. Referencing my comments above about the nature of character references, the employer isn't expecting a defense of your position - they're just expecting an honest and direct answer.
Finally, you made some additional comments which aren't questions but beg for answers:
I'd really like to provide him with a character reference that would help him land this job but I'm struggling to word it in a convincing way that doesn't sound like we're just a bunch of kids who play computer games together. I mean we're both middle aged adults with professional careers.
Keep in mind that it's not your job to get him this job, and ultimately your character reference will be one (fairly minor) data point used in the process. The employer will likely already know the guy isn't a time-wasting video-game playing kid - don't worry about defending his employability!
