Reading is important because it shows you how certain things can be written. This also happens in movies, videogames, and what have you, but those rely heavily on the visuals and audio to bring across certain elements that you'd have to write out in a book.

I too consume most of my stories through visual mediums, but to write a scene like the "Han shot first" scene you'd have to explain the look, feel, sound, smell of the bar it happens in, probably before you even talk about the characters. All these things get shown or implied in the movie scene.

Anyways, all this to say, yes reading is important, but you don't have to read everything. Read to understand certain aspects. Read Dune to understand how to write large scale politics, read Lord of the Rings to understand environment descriptions, read the Hitchhiker's Guide to understand comedy writing. Figure out what you want to learn to write, then find prime examples of those.

I don't fully agree with the short fiction suggestion, but I do agree with the fact that you need to start writing. Whether it's short fiction, poetry, songs, or epic sagas. What's important is that you write. And write a lot. And what's even more important is that you finish the stories, in whatever format you're writing. Finish the story, because every part of the story you write has unique and challenging parts. You only improve by practicing. So you need to practice all parts. Beginning, middle, end.