A lot of fantasy settings, whether in fantasy novels or a campaign of Dungeons & Dragons, are pretty human-centric - understandably so, since every player of a tabletop RPG (at present) is likely a member of the species Homo Sapiens. The tabletop roleplaying games below, in contrast, have settings where humans are vanished, extinct, or simply absent from the narrative - giving non-human species a chance to take the spotlight of the story.
In most tabletop RPGs where players can choose different races during character creation, humans are the "generic but versatile" option - lacking any special biological traits or stat boosts, but capable of being used to create nearly any character build. Some tabletop RPG designers have critiqued this RPG design approach for making humans the "boring" option, while others worry this approach implicitly presents humans in an RPG as the "superior species," while also, ironically enough, dehumanizing other races as one-note stereotypes.
By creating fantasy settings where humans as a category of species aren't around, the following tabletop RPGs are designed to side-step the awkward implications of making humans the "average" option in their character creation rules. These RPGs also give their players more chances to immerse themselves in the mindsets of relatable nonhuman beings with different cultures, instincts, and views of the world - a valuable thought-exercise for any potential future where the human species has to co-exist with nonhuman sentient beings.
ICON
ICON, a heroic fantasy roleplaying game designed by the creators of the sci-fi mecha RPG Lancer and the New Weird webcomic Kill Six Billion Demons, takes place in an Arcadian world of scattered settlements and city-states, with players taking on the role of mercenary treasure hunters and wandering heroes who delve deep into the churning, monster-infested dungeon facilities left behind by the long-fallen Arken Imperium. The Final Fantasy, Monster Hunter, Shadow Of The Colossus, and Legend of Zelda franchises were all big inspirations for the setting and tone of ICON. In particular, the humanoids seen in The Legend of Zelda: Breath of the Wild seems to have inspired the different non-human "Folk" and "Kin" types players can choose from during character creation: the insectoid Xixo, the Beastfolk, the Ogre-like Troggs, and the elf-like Thrynn.
Wanderhome
Wanderhome, a pastoral RPG about wanderers in a world of talking animals, draws thematic inspiration from The Wind In The Willows, the Redwall books, and the films of Studio Ghibli in equal measure. The history and landscape of setting is marked by hints of epic past wars and heroic quests to save the world, but players in a session of Wanderhome will mainly be journeying to new places, experiencing the changing seasons, and learning about the lives and stories of the varied animal-folk they encounter on their travels.
Realms Of Pugmire
The Realms of Pugmire tabletop RPGs used a modified version of the Dungeons & Dragons fifth edition rules to tell stories about a far-future Earth inherited from a vanished humanity by sentient, genetically uplifted domestic animals. In the original Pugmire RPG, player take on the role of heroic sentient dogs who re-claims relics from the ruins long-fallen human civilizations, fend off the demonic forces of the "Unseen," and try to "Be A Good Dog." The Monarchies of Mau spin-off focuses instead on the sentient cats of the Pugmire world, who belong to a culture steeped in political intrigue, a reverence towards necromancy, and the spiritual belief that each cat goes through a cycle of reincarnation with "Nine Lives" in total.
Sources: Realms of Pugmire