Where is this piece of music from?

There is a neat tune (edit: reuploaded) on YouTube uploaded in 2013, called the "Main Theme" of The Witcher 3. Judging from the date of upload, it might as well be fan-made, but it sounds really polished. Some people in the comments claim that this was from the first trailer, but I was not able to find any trailer containing this music.

Is this tune official? Where is it from?

While possibly not the first trailer, this music piece definitely came from A trailer. The trailer referred to is the "Beautiful World of the Witcher" trailer:

This trailer was released in 2015, well after the release of the video you linked.