Gender analysis is a type of socioeconomic analysis and has commonly been used as a tool for development and emergency relief projects. Most famous frame works of Gender analysis are Conversation Analysis Framework, The Harvard Analytical Framework, Gender Analysis Matrix, Social Relations Approach.My point of view Gender analysis aims to achieve equity, rather than equality

I really agree with your view on equity ... Thank you so much Kiran!

Beyond Jesse Fox's points, Rosalind Gill's «Gender and the Media» book has quite a few overviews of different methods by which analysis can be performed.

I would look at 'performativity' as a a theoretical concept. Judith Butler contends that gender is something that we perform/practice, rather than a solid construct or fixed reality. Considering that your research is in the realm of fantasy I think that she would enable you substantially. Butler is well known for discussing 'Drag', cross dressers, and how through their overt performance of gender they illustrate how fragile the dichotomous ideas of gender we have, are. 

I also think that a theory which looks at embodiment would be useful, especially if you are considering games in which you embody another body in order to gain access to and engage in the activity. Foucault is always useful when considering bodies but for your purposes you might also find Connell useful (in considering hegemonic masculinity). I personally love Sara Ahmed very much and her idea of stranger (see strange encounters). This might help you if you want to consider how different characters within the game interact with each other and how ideas of 'good' and 'bad' are embodied in these characters. 

Hope this helps :)

As already mentioned it depends on what you want to analyse. But I would suggest the work of Maria Nikolajeva https://www.educ.cam.ac.uk/people/staff/nikolajeva/. It might sound a bit odd since she worked on picture books, but there are many similarities.