If I understand correctly the only thing I have to do to use the .mo files is to set the the website language in the WordPress dashboard under "settings" to "Dutch". That was already the case so I assume I would automatically use those wpforo language files, right? But even in that case the "Welcome back Nico!" message appears in English 🙁

Yes, the better way is using PO/MO files. The wpForo built-in Phrase system is developed for addons and for quick translations.

As per the welcome message we could login and check it if you could send admin login details to support[at]gvectors.com email address.