Looking at my current prospectuses, I see that I tend to use two different techniques for achieving greater specificity:
Phrasal descriptors: not “science fiction” or “fantasy” but low fantasy, contemporary fantasy, dark fantasy, pulp science fiction, hard science fiction, streetlevel supers, four-color supers.
Compound descriptors: mentioning several different categories that a campaign falls into: hard science fiction/alternate history, near future weird/dark fantasy, alternate history/swashbuckling/martial arts, realistic fiction/workplace drama/soap opera.
It seems to me that the category of “genre” as used by publishers, bookstores, and libraries is based on several different classes of attractors. There is the presence and nature of fantastic elements, as in “science fiction” or “fantasy.” There is the kind of emotional appeal, as in “horror” or “thriller” or “romance.” There is the type of plot, as in “mystery” or “erotica.” A marginal case is the historical setting, as in “Western” and “Regency romance” and perhaps “steampunk” (which isn’t simply fiction with fantastic elements, but fiction with fantastic elements that is set in a specific historical period)—a lot of historical settings are not broken out as distinct genres in this way, but simply lumped into the broad category of “realistic fiction,” which is not usually considered to be “genre” but which for the purposes of RPGs probably should be so regarded, not least because it’s a minority interest that needs to be called out as such. This perhaps exemplifies a broader point that not all of the categories of “genre” in print fiction or film/television/video are equally useful for defining an RPG campaign.
In GURPS, for example, there is a category that could be called “genre books,” meaning guides to how to adapt the core system to specific genres: fantasy, horror, science fiction (in GURPS Space and the soon to appear GURPS Future History), supers, or the perhaps narrower categories of action/adventure, dungeon fantasy, monster hunters, and postapocalyptic. I think the existing books cover most of the viable categories for gaming (the previous edition had a genre book for cyberpunk, but I think that has largely died back or been merged into science fiction again). At least, I find it hard to think of new genre books to propose that would be likely to have wide appeal. I’ve played with the concept of GURPS Utopia/Dystopia—fiction whose fantastic elements are justified not by appeals to science nor to myths and legends, but to ethical ideas—but I’m not sure this would have wide enough appeal to be marketable. Though it does occur to me that a “workplace drama” book (the large category that includes police procedurals but not so much other mysteries, and that also includes series about hospitals, law firms, and even taxi companies and radio stations) might be of interest to a lot of GURPS aficionados—but it would need someone with broader experience than mine to write it.
I have to note that science fiction critics used to point to this sort of thing as a failure mode for science fiction: the Western, or detective story, or romance, or Graustarkian adventure that was transposed to another planet, but with no actual scientific ideas that went beyond terminology (“call a rabbit a smeerp,” as TV Tropes has it). I wouldn’t want to say that doing this is necessarily a failure, but I’d like to see some discussion of how to avoid that kind of failure. For example, I lately picked up Malcolm Jameson’s Bullard of the Space Patrol, which I read back in the 1950s, but I found myself bogging down, largely because it became evident to me that Jameson was telling stories about naval service (for example, one about white mutiny) with a veneer of science fiction.