Two things might have gone wrong:
- the app is quarantined by Gatekeeper because it's from an unknown developer;
- the executable inside the app might have lost its execute permission during unzipping
To check quarantine, start Terminal and type "xattr " without the quotes at the prompt and drag the TheTwist049MAC app into the Terminal window. Terminal will fill out the path for you. Mind there is a space between the command and said path. Hit enter. If you see
com.apple.quarantine in the results, the app is quarantined.
To remove the quarantine, type "xattr -d com.apple.quarantine " and drag the app again into the window. Hit enter. Quarantine should now be removed.
To check the second case, you need to look into the contents of the app: right click on TheTwist049MAC app, pick Show package contents. Navigate to /Contents/MacOS/. Inside that folder you'll see a file TheTwist049MAC. That file should be a Unix executable. If it's anything else, it has lost its execute permission.
To fix this, start Terminal and type "chmod a+x " without the quotes at the prompt and drag the file inside the Terminal window. Terminal will fill out the path for you. Again mind there is a space between the command and the path. Hit enter. The file should now be executable.
As a general precaution, make a duplicate of the app first before changing its attributes or permissions.