Nintendo hasn't had the greatest track record in supporting LGBT options in video games. Although, Birdo from Super Mario Bros. 2 is arguably the industry's first transgender character.
Recently, the release of Fire Emblem: Awakening on the Nintendo 3DS included marriage as a gameplay mechanic but only via one man and one woman. Needless to say, it sparked debate as the mechanic only existed as a means to procreate.
Furthermore, Nintendo appeared to establish their point of view on the matter when they removed the ability to participate in same sex relationships in the Japan released game, Tomodachi Collection: New Life for the Nintendo 3DS. They viewed this feature as a glitch and patched it out. Note: Japan does not recognize same sex marriage either.
Famed game desinger and producer at Nintendo, Shigeru Miyamoto had this to say in an interview with Kotaku's Stephen Totilo, "So, if we end up creating a gameplay structure where it makes sense for, whether it's a female to go rescue a male or a gay man to rescue a lesbian woman or a lesbian woman to rescue a gay man, we might take that approach. For us it's less about the story and more about the structure of the gameplay and what makes sense to be presenting to the consumer."
There is hope yet, but your prince/princess/gender-neutral-royalty is still in another castle.
Click the link below for the full interview from Kotaku.