"Rzeczpospolita" is a calque translation of the Latin expression "Res Publica". From what I remember from Latin classes, it means "common affair/public matter".
The point is that "Rzeczpospolita" doesn't mean "Republic". It clearly means "Commonwealth". In the polish language, any other republican state is referred to as "Republika" (Republika Grecka, Republika Francuska). So, modern Poland didn't change its official status since then. It's not "Republika Polska", but "Rzeczpospolita Polska". So it was then, so it is today. Why the official title abroad is "Republic of Poland", I do not know. A horrible mistake, or joke. Normally, it should be "Commonwealth of Poland", even if that country, today, lacks the Lithuanians, Ruthenians and numerous other ethnical groups that made the Commonwealth a phenomenal multicultural state. Also, the first real modern democratic state, before even the term "Republic" was coined for the needs of international relations.
Finally, the initials of Poland are "RP". In the popular view, it's the acronym of "Rzeczpospolita Polska". In reality, these initials were used back in the 17th-18th century on an international stage, to refer to the "Res Publica", a unique state by any standards.
"The Crown" and "The Grand Duchy" were terms used mostly within the borders of the Commonwealth. Ethnical Poles would most often be referred to as "Koroniarze" (sing. Koroniarz), as for those that come from the "Korona". Often, the Grand Duchy would be simply refered to as "Litwa", just as the Kingdom could be with the use of "Polska".
The King (who was something similar to the modern President of the United States, judging from the political system in the Commonwealth) held both titles of Rex and Magnus Dux, along with several other, minor and most often personal titles.
For example, the titles of Władysław IV Waza (the King preceeding the one in the game) were these:
Vladislaus IV, by the Grace of God, King of Poland, Grand Duke of Lithuania, Ruthenia, Prussia, Masovia, Samogitia, Livonia, and also hereditary King of the Swedes, Goths and Vandals, elected Grand Duke of Moscow.
Yup, that was a guy I'd want to hang out.
Here's a link to the Grand Coat of Arms of the Commonwealth:
http://upload.wikimedia.org/wikipedia/commons/8/8c/Coat_of_Arms_of_the_Polish-Lithuanian_Commonwealth.svg
And here's a link to the Royal Banner, from the seven year period where Poland and Sweden were under a personal union, together forming the only historical, unique superstate that had the Baltic Sea as an internal lake:
http://upload.wikimedia.org/wikipedia/commons/5/59/Flaga_Rzeczpospolitej_Obojga_Narodow.svg
Dominum Maris Baltici wasn't that hard afterall, eh? Too bad things went wrong afterwards.
So, either "Polish-Lithuanian Commonwealth", or "Res Publica". Or go hardcore and use the official Latin name.