First, you don't need to wait for recruiters to contact you. There are plenty of websites that post software developer job openings that you could scan through and proactively apply to.
Second, I would nuance or clarify your technology list. It seems unlikely that you have actively used Java, C, C++, C#, PHP, And HTML all in equal measure. Make it clear which ones you have used most.
Third, remove the part about looking outside the game industry. People are more interested in what interests you than what doesn't interest you. Give some thought to some general or specific types of development that might interest you and mention those instead. For example, scientific software, database software, backend, front end, or even just working in an agile shop.
Last, don't despair. At 3 years, you're no longer junior, but you're far from having typecast yourself as a game developer. In your position, you don't have 10 years of experience in a prospective employer's domain and/or technology so and they will not be looking for that in you. Instead, it's more important to demonstrate you can learn and adapt quickly. If anything, being a game developer should be a positive here as the game developers have a reputation for being clever.
EDIT: To touch on the discussion in the comments: Regardless of the industry you apply to, you need to make a compelling case to potential employers that you are a good fit for their company. You can best do this before an interview by writing a targeted cover letter. You can also have a bit of a pitch prepared for interviews.
As a developer with 3 years of experience, you should focus your ability to adapt, ability to write good, clean, well tested code, solid understanding of computer science fundamentals, and real-world software engineering experience. You should try where possible to give examples of these.
Additionally, you should spend some time understanding the companies you apply to. What industry are they in? What types of software do they need or develop? In your cover letter and in any interview, you should include some details about why that interests you and how you might make a contribution in those areas.