The answer to your question is "Yes, if your skills and experience are transferable to the role you want". As an example, full stack/web developer experience would be relevant if we were hiring for a browser game or to build us a web interface like the World of Warcraft Armory. Full stack/web dev experience would not translate to doing environment art or combat design because none of the skills that candidate brings to the table would be applicable to the role.
Remember - when we hire for a position, it is because we have a bunch of work that we need someone to do for us. We want to find a person who we believe will be good at doing that work. Relevant experience doing similar work is the best indicator that a candidate will be able to do it. If you want to leverage your non-gamedev experience in the game industry, look for a position where that non-gamedev experience would be applicable, rewrite your resume and cover letter to show us how your experience applies, and apply for that position.
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