Couldn't agree more
You're either born as a good problem solver and therefore make a good programmer - or you're not
There's so many coders I've worked with in the last 15-20 years that just can't naturally solve problems and end up writing tons of pointless spaghetti code that's impossible to maintain.
As others have said I'd learn the basics of C, the chances are if you do become a game developer these days it'll be on a mobile platform like iOS or Android or a web platform. Console gaming is nearly impossible to get into.
90% of languages you'll use (Objective C, C#, PHP etc.. etc..) all come from a C background - so it's a nice generic low level language for you to learn to program in. If you learn specifically C# you'll already have locked yourself into a certain type of coding - and I wouldn't do that until you've had a bit of industry experience to be honest
I've coded in PHP, C, C++, VB, ASP, ASP.net, Javascript/Jquery, Cobol, Foxpro, Pascal, Basic, 8086 Assembler, Lisp ..... and probably a load more i've forgotten lol took me a good 4-5 years to settle down into a language I find flexible enough for my needs