backing up the exe and dll (and ocx for the web server) files and replace them with the new ones is a safe way to upgrade from 1.4.12. You can also safely replace dgate.dic.
Do NOT replace or remove dicom.sql. If you do this, a full database regeneration is required. Other files contain yoiu
Naturally the server must be stopped before files can be replaced. In case the server runs as a service it must be stopped using the control panel or by un-installing it as a service.
Another safe option (which allows experimentation with the new version) is to install 1.4.14 completely anew, stop it, edit dicom.ini so that MAG0 points to your old data, and regenerate the database.
The zip files are just zipped old log files - you can delete them or move tjem somewhere else.