Game designer is a different career path than programmer. If you have mobile games in your career history it certainly won't hurt you.
Game designer is not an entry level position. Any portfolio you build will start with a list published, shipped titles. In addition to shipped titles, good game designers have a passion for games, and their experiences often include game modding, CCGs, board games, D&D-style games, tabletop games, and a experience with a wide variety of genres. (Those are "and", not "or".) A good designer is a writer and a presenter, a logician and a debater. They can instantly jump from making a strong emotional game pitch to a CEO to describing the intricate mechanics of why a specific set of dice rolls is necessary for a specific circumstance inside a game. They can explain why a specific music style is necessary for a specific game situation. They can explain why a specific art style is necessary for a specific game situation, and if they are given an art style and a situation they can design a game around it. Often game designers are given a set of fairly tight constraints and then told to build a fun game within those constraints; it is very hard work, but many find it fun.
There are some lesser design-related positions that are available earlier in the career, but "game designer" usually requires years of industry experience and a passion for creating fun games outside of the work environment.
Tom Sloper's articles cover the differences between the jobs here for designer and here for programmer.
Edited by frob, 16 January 2014 - 09:23 AM.