Genre emulation in tabletop RPGs, as I understand it, is the attempt to write game rules that when followed result in play experiences congruent with the genre being emulated. More specifically, the fictional events that occur and stories generated retroactively should conform to various genre patterns and expectations. For example, the rules of Pendragon are designed to result in stories recognizably similar to Arthurian romance, the rules of Monsterhearts are designed to result in stories recognizably similar to young adult contemporary fantasy, and the sanity death spiral of Call of Cthulhu intends stories in the key of Lovecraft. This allows game designers, and so referees, to leverage shared meanings.
Despite this benefit, games that attempt to emulate genres flexibly tend to be somewhat bland. While this might read as a criticism, and it is to some degree, it should not be surprising considering that genre is, at some level, structure without flesh. The horror genre is the collection of structures and properties shared by, for example, The Exorcist, Psycho, and Night of the Living Dead. This means that the referee, or gaming group as a whole if setting and narrative responsibility is shared, must add this layer of aesthetic detail atop the genre-supporting framework or be satisfied with a more stereotypical or conventional realization of whatever genre is being emulated. Every dwarf gruff, every elf haughty, and every private eye cynically jaded. Even though such direct reliance on genre can sometimes result in elements of questionable uniqueness, the now widespread availability of many different genre emulators is a real advance for players desiring such tools.
However, for those not satisfied with more agnostic toolkit rule systems but also lacking enthusiasm for genre emulation, another option would to be prioritize what Ynas discusses as thematic concerns. Tabletop RPGs have always had aesthetically engaging settings such as Tekumel or Dark Sun, but this thematic approach, which may be somewhat recent, blends setting with rules while still building on recognizable frameworks. This approach leverages as many commonly known elements as possible to communicate setting flavor and may use rules to generate setting details rather than taking an encyclopedic approach. For examples, consider the character creation rules of a Thoroughly Pernicious Pamphlet and the tables constituting the setting of Yoon-Suin.
Some additional recent standouts taking this approach: