Similarly, if you, "Try to make a game for American culture," which involves a lot of actual text and storytelling is a big focus of the game (such as an RPG, an adventure game, or a VN) and you are not fluent in both English and the culture of America or the West, then you could be shooting yourself in the foot.
Very much this!
I worked on a project (years ago) that had areas set in parts of the world I have never been. Researching those backgrounds (just the backgrounds) was a HUGE undertaking. Sewer grates look different, road signs are different, traffic lights are different, the shapes of the curbs are different, the way the lines (if there are lines) are painted on the roads is different... I mean it's amazing how similar, yet different, the world can be and I realized that any native of the area would probably know that the background wasn't created by a fellow native simply based on tiny little details that would be very easy to get wrong (even with a lot of research).
To answer the question posed though, I am not sure if I could even define a "universal" culture.
That being said; the way America is these days (and in recent years) I'm not sure I'd
want "universal" culture to reflect it!
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and YAY 
!!