@sviiseven oujo refers to a kingdom's princess, a royalty. luna is just a duke, which are usually related to royalty but not technically royalty. are you sure it's not ojou-sama instead? ojou usually refers to a lady. they also should have different kanjis. 王女様 and お嬢様
Using chess as analogy only makes sense when both players normally alternate turns, despite the difference in speed (if any). When "how often you get a turn" is quantified in numbers, you have to refer to turn gauges instead, which basically is a bar that fills up according how fast your...