Hi PhotographerBerlin,
Welcome to Affinity Forums :)
The retail version is installed by the App Store app itself so i believe you're referring to the Trial.
Have you downloaded it from Affinity's official site? If not i advise you to sign-up here and download it from the link that will be sent to your e-mail.
Hmm, given that it’s distributed via the App Store I suppose the security setting shouldn’t matter but perhaps it’s still worth to try to change the settings for downloaded apps:
System Preferences > Security & Privacy > General > Allow applications downloaded from > Anywhere
(Systemeinstellungen > Sicherheit > Allgemein > Apps-Downloads erlauben von > Keine Einschränkungen)