I found a solution to my problem, and just want to post it for further reference.
NPIdentifier screenId = browser->getstringidentifier("screen");
NPIdentifier heightId = browser->getstringidentifier("height");
NPIdentifier widthId = browser->getstringidentifier("width");
NPObject *window_obj = NULL;
browser->getvalue(mNPPInstance, NPNVWindowNPObject, &window_obj);
NPVariant screen_var;
browser->getproperty(mNPPInstance, window_obj, screenId, &screen_var);
NPVariant height_var;
browser->getproperty(mNPPInstance, NPVARIANT_TO_OBJECT(screen_var), heightId, &height_var);
NPVariant width_var;
browser->getproperty(mNPPInstance, NPVARIANT_TO_OBJECT(screen_var), widthId, &width_var);