Would like to transfer app from old computer to new one.
If you bought via the Mac App Store, make sure you're logged in at the Mac App Store app with your Apple account. You can check if the icon on the lower left shows you name.
If it doesn't show your name, you'd need to login via ⌘0 where you can also see all of your purchased apps and can download Mp3tag via the respective icon.
If you bought a license via my website, you need to enter your license details on the new computer to register the trial version.