I’ve found out something that might help debbugging the problem.
If I am on the en ‘game’ post type editor, I change the year field and I press update, the field on the translations does not change. However if, in the same page without changing anything I press the update button again. The fields are propagated and the values are synced between translations.
This might be stupid, I haven’t checked the code but can it be that the propagation/syncing is being done before the values are stored?