The draft that has fallen into your hands is most likely a copy of Stephenie Meyer's next book, Midnight Sun. You are correct in assuming that this book is Edward's version of Twilight. You are also very right in assuming that the copy that you have is illegal. It is for this reason that Midnight Sun almost didn't happen.
According to Stephenie Meyer website, this version of the story was released and is being circulated without her permission and is of poor quality. She says:
"I'd rather my fans not read this version of Midnight Sun. It was an incomplete draft; the writing is messy and flawed and full of mistakes"
After this version was leaked, Meyer decided not to complete Midnight Sun. However, after receiving many, many emails and letters from fans. Meyer has decided that she will in fact complete the book. No release date has been set as of yet. Still, true Twilight fans know that Stephenie Meyer will deliver a story that was well worth the wait. Until then a copy of Midnight Sun authorized by Meyer can be found on her website. Happy Reading!