What makes The Castle of Otranto a Gothic fiction?

The Castle of Otranto is considered the Ur-text of all subsequent gothic fiction, as it established many of the tropes and imagery which would come to define the genre. Here are a few of them:
It takes place in an exotic past. For the eighteenth-century audience, the Middle Ages was a distant time period associated with pre-enlightenment attitudes. For the specifically English audience Horace Walpole was writing for, the Catholicism of these characters was another exotic element, as England was firmly Anglican by this time. This lends the story both an escapist element and a sense of the unfamiliar.
It focuses on terror and suspense. From the beginning of the story, Otranto's atmosphere is steeped in foreboding and dread. Gothic fiction is known for inspiring feelings of unease in its audience, even sometimes through the setting alone. Characters are thrust into uneasy situations: being trapped in a dark castle, being threatened with violent acts, and being frightened by supernatural elements.
The characters in Otranto have plenty of reasons to be terrified: Isabella is threatened with rape at the hands of Manfred, Manfred is terrified of supernatural forces which seek to end his line, and Theodore is almost killed by Manfred's insatiable paranoia and tyranny.
It combines the uncanny with depictions of normal life. While much of Otranto might seem outlandish today, what made it unique during its original publication was its combination of supernatural terror with grounded characters and setting. This is no fairy story, but a relatively realistic medieval setting with characters who largely possess some depth to them (particularly Manfred and Matilda). This element of gothic literature would be much more emphasized in later incarnations of the genre, such as in the gritty setting of Wuthering Heights or the realistic London streets of The Strange Case of Dr. Jekyll and Mr. Hyde.
It features supernatural elements. Otranto's titular castle is a labyrinth of dark corridors, doors that open and shut of their own accord, paintings that move and sigh, and other such bumps in the night. Inspiring fear in the audience has been a big part of gothic fiction's legacy, and Otranto did that thoroughly for its original audience.

Walpole's Castle of Otranto is considered the first Gothic novel and contains many of the elements that would become standard in Gothic fiction.
For example, the story takes place in the Middle Ages and is set in a suitably creepy and mysterious castle complete with secret passages, towers, and trapdoors.
Further, the novel merges a realistic story with supernatural elements. These include a giant helmet falling from the sky and crushing Manfred's son Conrad, the animated portrait of Ricardo, doors that open and shut by themselves, and frightening, mysterious sounds. Many of these elements (though not the giant helmet) have become standard features of Gothic novels.
In addition, the book features a cruel and frightening paternal figure in the character of Manfred, along with a female who has to escape the clutches of the cruel male. In this novel, it is Isabella, who was engaged to marry Conrad before he was crushed. She has to escape Manfred when he decides to wed her against her will. In another motif typical of the Gothic, she takes sanctuary in a church and is protected by a friar.
Finally, the novel is characterized by an atmosphere of fear, foreboding, and terror, perhaps the chief characteristic of the Gothic genre.