IOS – Does free iWork on iOS entitle me to free iWork to Mac

This seems to be a strange issue. So I do not have any solutions to fix them as it exists on the system. Before you proceed, ensure that you create a backup (using Time Machine or a disk cloning tool like Clonezilla, Carbon Copy Cloner or SuperDuper!). In case things get worse, you can at least revert to the last known (better) state.

You can do one or both of the following:

• You can reinstall OS X yourself. Hold Cmd+R on startup to get into Recovery Mode and select the reinstall OS X Mavericks option.
• If you have a backup with Time Machine from before the upgrade, you can also choose Restore From a Time Machine Backup from the recovery options, select the date/time of that backup and go back to OS X Mountain Lion.

Also see OS X: About OS X Recovery to use Recovery Mode (this is applicable from OS X Lion onwards).

Whenever buying anything from Apple in the recent past that came with software, it's been linked to my Apple ID, so perpetually available in the App Store.

Eg. buying a Macbook just as Mountain Lion came out, it shipped without it, but was available for free from the store with it when I logged in with my Apple ID.