Whew. Let's take this one at a time:
Coming-of-Age: Well, this one's a freebie. Pip is a scared little six-year-old at the beginning of the novel; he's a grown-up man at the end, and the whole book is about how he gets from point A to point B. In fact, Great Expectations is pretty much your classic Bildungsroman: a fancy German word for a novel entirely devoted to telling a coming-of-age story.
Gothic fiction: Creepy house. Creepy old lady. Ghosts. Long-lost prisoners. And did we mention the mist? Sounds like Gothic fiction to us!
Realism: Ooh, now we're getting excited. If we were asked to describe the plot of Great Expectations in ten words or less, we could say this: "a very long story about a boy who grows up." Or we could say this: "a three-part story about unrequited love." Or we could say this: "a serialized novel about a boy and an escaped convict." Or this: "it's about a little boy who meets a crazy lady." Or perhaps the following: "a tale of a boy who betrays his best friend." Or even this: "a story about how Victorian society is wack." And we think even this one would work: "a story about beer."
The point is that there's a lot going on in this big, fat novel and, while Pip is most definitely the object of our affection and attention, Dickens doesn't hesitate to cram in every detail possible about the world around Pip, thus leaving us with a good sense of the everyday, realistic details of a specific time and place. And that, Shmoopers, makes it realism.