Rige encompasses the many terms you can have for a country, though it does not directly translate to country, but more things like kingdoms, empires and such. Interesting things to note is that it comes from the danish word "rig" which means rich, possibly denoting wealthy countries? And a kingdom specifically is kongerige (king - rige). Interestingly, the closest word I could find was the german "reich"
Very similar to ‘rijk’ in Dutch and ‘reich’ in German
It is the literal translation of realm.
Swedish: Rike
German: Reich
Spanish: Reino
English: Kingdom is the right translation 98% of the time, empire or realm are other possibilities.
Rige, I would say, comes from the / or at least origins from same place as, the german word reich