Don't apply to just game companies. If its your first industry work experience, you'll learn a lot pretty much anywhere you go. Customize your resume for companies you really want, and have a generic one for the rest. Rapid-fire your resume to all companies you can think of. Even if you don't want the job, get software eng interview practice because software companies all have very similar interview questions. e.g. the interview process at Valve is very similar to an interview at Google or Facebook.