I am well aware of the Star Charts book (I have a copy of it myself, in paper form). I am also well aware of how the game depicts the sectors/sector blocks. Nevertheless, the book (thou it's regarded as 'soft' canon), is NOT de facto canon. In fact, the book does the same mistake as ancient humans did, when they believed that Earth was the center of the universe.
Earth is located in the Alpha Quadrant. Not Beta. Not next to Beta, and certainly not half/half Alpha and/or Beta, as depicted in Star Charts.
In fact, move the thick orange line 1 sector to the right, and suddenly planets seem to match up a hell of a lot better. In other words, Sirius Sector Block in ALPHA Quadrant.