Agreed, I have received an answer from the kind Simon Carless from Mobygames:
Thanks! We are not permitting API use for plugin users right now because that will be a lot of work for us to individually approve API use manually for LOTS of users, sorry. We will be allowing plugins that grab images to their own database and allow Launchbox users to access them there. We have had multiple Launchbox plugin authors contact us recently so we imagine one of them will sort this out soon.