Societies where low life quality is justified by potential mobility fail the test hard. They are desirable only if you assume you are one of the few able to take advantage of that mobility to get out of the undesirable positions in society. Such an assumption is not possible in any interpretation of Rawls I've seen. If you were able to assume you are in such a privileged position you may as well assume yourself to the top of the pile in the first place.
A theoretical society where absolutely anyone can always improve their situation without compromising on other aspects of life and where it is not at the expense of others
might pass. But that doesn't reflect reality in the slightest, not least from a limited resources point of view. A guaranteed minimum quality of life is considerably more possible than unlimited social mobility.
So what system of rules or incentives or whatever, if any, would we want to set up regarding video game diversity? Assuming we had full power to set up whatever system we wanted, and if we didn't know ahead of time which of those relevant people we would be (with all of their OWN biases and preferences you must consider, which are likely not the same as yours-as-you)?
I don't think talking about rules is helpful, but rather outlining what would be desirable as a member of society (in this case, the gaming community) might be more interesting. Just speaking for myself here, and I'm probably missing a lot;
Community: To have a sufficient range of communities in which I feel welcome. Sufficient here meaning wide enough to encompass any genre/subset of games I might be interested in, regardless of any historical trends in those genres.
Representation: To have a wide range of archetypes and stories told about people like myself. To see representations of myself limited to stereotypes or only a few acceptable archetypes. To have redemption arcs and tragedies and romances and heroics and whatever other stories you can imagine told about someone who represents me, so that these stories can be seen as genuinely universal stories about humanity, not just the subset of humanity currently seen as the default main characters.
Industry: To have no biases (personal or institutional) as to which positions in the industry might be available to me outside of talent, ability and experience, with this assured by seeing people like myself throughout all roles and levels.
As to ways to address these, that's harder.
The first requires continued fighting against bigotry among gamers and efforts to clean up the bigger communities. There has been a fair amount of effort dedicated to establishing new communities with those values baked in from the start, which goes a long way but not far enough. A lot of the time if you want to play a certain type of game you are forced to take part in the built in community. There is also the risk of ending up with effective ghetto communities of minority gamers which are used as an excuse for the mainstream to remain exclusionary.
The second requires stories about non-default characters to be told as often as stories about the default. This just means having more and more games made where diversity is just an accepted part of how things are. No easy way to get there, just something that needs to keep happening over an extended period of time.
The final is a matter of cultural shifts in the industry, and probably some element of affirmative action (at the least active campaigns to promote the industry as a career path within minority groups). PR is an aspect here, but without the changes being real and not just wallpaper then it will likely not work.