Numenera
Monte Cook Games' 2013 debut release Numenera is included in this survey primarily as a counterpoint to the intrigue rules of SIFRP and to demonstrate that the elaborateness of persuasion mechanics in a role-playing game correlates strongly with how important social interaction is to its respective core fantasy. Whereas SIFRP , with its emphasis on courtly intrigue and conspiracy, dedicates an entire chapter to persuasion mechanics, Numenera focuses primarily on mystery, exploration, and the awe of discovery, so the entirety of its social interaction rules fits in a single paragraph.
Said paragraph is found on p. 104 of the core rulebook, in the subsection "Interacting With Creatures" of the section "Action: Do Something Else" under the combat rules. The game features three primary stats (Strength, Dexterity, and Intelligence) and social interactions use its core mechanic in combination with the Intelligence stat. The specifics of said core mechanic are not relevant to this survey (given Cook's previous work on 5E, it is unsurprisingly similar to, yet distinct from that of D&D). More important is the fact that by not attaching any ludic procedures beyond the core mechanic to in-fiction social interactions, Numenera contains an example of the smallest possible social gameplay system. The only way to make it even more lightweight would be to leave social interactions entirely up to role-play and player fiat, which would effectively bypass the ludic layer entirely (as is the case, for instance, in Fiasco).