Feminist theory is much more than just the pursuit of gender equality, it is the questioning of the very power dynamics and institutions which sustain inequality in general. Feminist theories decode how identity influences a person's decisions and their relationships with others, and places these behaviors and interactions within the context of the environment and culture they participate in. With such an approach, a feminist lens is useful for just about any situation.
While feminism has a history of Western dominance, it still certainly has a role to play in developing countries. That role, however, will differ from community to community and person to person. In Somalia, feminism can mean encouraging more women in political leadership. For some in Latin America, it can mean challenging harmful trade deals. For some in post-communist countries, it means challenging the empty rhetoric behind a superficial pursuit of gender equality. Perhaps most importantly, it's the understanding that a few cannot speak on behalf of all, and while we can tap into a collective power to resist subjugation, each individual life experience has its own story to tell.
Feminism, of course, can contribute to shifting the pay gap. It's a mechanism to make available greater equity of opportunity - which includes creating both parity in wages and parity in job opportunities. Not only do women get paid less, but women face greater structural barriers which prevent them from reaching the highest levels of leadership in most fields. Feminist theory provides the tools and perspectives to take a critical look at the patriarchal tendencies which allow such an injustice to perpetuate, and challenge the status quo. To learn more about the wide array of feminist theories, see The SAGE Handbook of Feminist Theory.