The Open Beta for Ever, Jane is not currently available through the Mac App Store. By default your Mac might only allow apps downloaded through the store. There are many good articles on the internet that detail the process of enabling apps downloaded from other sources, however here is a summary of that process.
1. Open "Security & Privacy" within the System Preferences.
2. With the "General" tab selected in this window, click the icon that looks like a padlock on the lower left corner.
3. Enter your username (if needed) and password and click "Unlock".
4. Change "Allow apps downloaded from:" to "Anywhere". The default setting is "Mac App Store".
5. Read through any important messages about this change and confirm you'd like to "Allow From Anywhere".
Our game client should now open correctly.