Greetings,
Apologies for those of you running into the issue reinstalling the FFXIV Mac client, but there is a known issue with Gatekeeper in previous versions on Mac OS X and it is not related to our software or license. While making temporary adjustments to the security permission levels will allow installation, it is not something that we would recommend doing as it creates a higher security risk. As we mentioned on the new client download page, we recommend that you update to El Capitan, the latest Mac OS, in order to rectify the problem.
We’ve also added this information to our FAQ as well.