Yeah, you should not remove your previous game (/installation/save files), just download and run/install the new files and the nessecary parts will be updated so you can play book 3.
I think if you removed the old ones you could loose your saved games etc.. The new file will update your old books to the newest/correct versions and install (the newest version of) book 3. :)
(If you would install just book 3 the old books may not be updated to the newest versions and they may not work good with the newer episodes.. Thats why the file updates all the books to the newest versions.)
Some other hints for starting book 3:
If your choises show wrong in the beginning of book 3, try beginning from the last save you made in book 2 and play it and then begin book 3 from the beginning.
If you can't download the new files, try refreshing your games library by clicking this link:
https://www.gog.com/user/refresh