Yes there are specific drivers for monitors - they often allow you to change settings and other features standard monitors do not have. The generic driver simply allows for the "standard" driver that applies the common generic settings all monitors have.
There should be an .inf file related to the .cat file -- the .inf file will identify which drivers files are necessary for your specific hardware.
My specific issue seems to be Windows 10 -- it could not migrate this monitor to Windows 10 - It was able to identify my secondary monitor (Samsung) and migrate its drivers.. the ASUS drivers however are being rejected by Windows 10 and ASUS does not have them listed as of yet.