Steam Share not giving me access to one of the games

As per the Family Sharing FAQ:

Can all Steam games be shared with friends and family?

No, due to technical limitations, some Steam games may be unavailable for sharing. For example, titles that require an additional third-party key, account, or subscription in order to play cannot be shared between accounts.

A game might not be available for sharing due to several reasons.
A little more info can be found here:

Free to play games and any purchased DLC for those games is also not supported for Family Sharing.
In addition, if your account has a VAC ban, you will be unable to share any VAC protected games.

Additionally, as stated here, "PC versions of Activision games will only be playable in the region in which they were purchased". Since the region you're playing in is checked through your IP address, using a VPN can also restrict your access.