I've been playing piano since I was 6, and by next November I will have been a playing concerts at various halls in NYC for 3. On the road, I picked up a wide knowledge of music theory. A plethora of chords and modes at your disposal certainly helps.
However, the most beneficial thing you can do (in my opinion) is listen to music, 24/7. (I'm surprised no one has mentioned this yet.)
Who's your favorite artist/band? Go explore artists of the same genre, and then some. And when you're done with that, go play some Celtic or Oriental music. This is a great approach to learning new modes without feeling like you're studying a science. Also, by collecting fragments of music here and there, you will find your own style. This is essential to writing moving music.
TBH, your improvisation didn't strike a chord in me at all. It lacks that factor because it lacks variety. So go ahead, learn music theory. But it's a long and hard process: methodical, not poetical, rigid, not fluid. It can be very daunting, and I'd hate to see you quit. Learning how to compose never has to be burdening.
It makes me happy to see aspiring musicians such as yourself. Godspeed.
http://www.youtube.com/user/kylelandry
Oh and study this man dutifully.