• Go to System Preferences > Security & Privacy
• Click the lock icon in the lower-left corner and enter your administrator username and password
• Under "Allow applications downloaded from", select "Anywhere"
You may also refer to the screenshot as below:
After that, you can launch and run Any Video Converter Free on your Mac OS X 10.8 & 10.9 normally.
Note: You can change the security setting back to “Mac App Store and identified developers” or “Mac App Store” as desired, for improved security.