Think of it like a tabletop RPG combat system (with dice) mixed with those old choose your own adventure books. Queen's Blade is along the same lines.
To my knowledge there's no plans for a videogame of it. Their next full game is Chaos:Head (yandere-heavy by the looks of it. I can't wait. It's gonna be awesome) and they have another Dra+Koi, but I don't think it's a game.
Actually, looking around it seems Queens Blade and Gate are used synonamously. So if you're looking at getting a book, search for both to get the best results.
True, but stores use them synonamously so if Hitmker or anyone else were looking for a book, stores tend to not label them properly so it's best to search out both names.