1. Check the disk
If it is the old MacSoft version then the disk will have MacSoft's trademark printed at the bottom, and it will be a CD, not a DVD.
If it is the new Aspyr version then the disk will have "Sid Meier's Civilization Complete" printed on it, it will also have 'aspyr', and it will be a DVD.
2. Check the application's file name
If you can't check the physical disk for some reason, then find the game application file in the Finder - the one that you can double click to try to launch the game, and not a shortcut.
If the file is called "Civilization 3 Complete" then it is probably the new Aspyr version.
If the file is called "Civilization III" then it is probably the old MacSoft one.
3. Check the application file's version information
To remove all doubt, right click the icon and select "Get Info" in the contextual menu; or left click it and select the File->Get Info menu option in the Finder's menu bar; or left click it and use the shortcut Apple-I on the keyboard. A window will appear containing information about that application file. Look for "Version" in the list.
If the version string starts with '1.22' (or possibly '1.27' if you've chosen the Play the World file) then it is the new Aspyr version.
If it doesn't then it is the old MacSoft version.