Ok, I found out how to fix it.
Bascially in the Default Apps page of the settings, one of the default apps ("video player" in my specific case) was empty because I had uninstalled the default app (planning on using MPC-HC instead).
I think that, for some reason, if the Default App field related to some extension is empty, the user cannot choose another program for that extension.
I just reinstalled the app I had uninstalled and reset the Default Apps to the defaults.