To see any kind of large scale roleplaying games developing, I think you need a critical mass of enough different things going. You need decent literacy rates, you need books/rules to be accessible which probably requires a large scale printing/publishing industry, but most of all you need to have a decent of amount of leisure time available. That last one is the biggest limitation, Tabletop RPG's necessitate a good deal of time commitment, so you need to have limited working hours and decent enough wages for that to be available. So without making bigger changes to the timeline, I'd say the earliest you might be able to get a TTRPG is roughly the early 20th century. I don't think nobility/gentry would be enough to sustain a tabletop industry, its already a niche hobby unfortunately, and a small niche for a small class of people that has fairly low margins doe not breed a successful industry.