Expect to have a game demo portfolio. It speaks much louder than your resume and degree. Of course the programming concepts you are familiar with can be transferred in making a game. Game programming is more about testing one's fundamentals about a graphics library on top of the algorithmic problem solving using the conceptual and fundamental knowledge of the language and following the software engineering principles to maintain and reuse the code-base and planning and project scope.
You should be able to modify and read other people's code.
Since you are familiar with C#, try mixing it with XNA or MonoGame to make a game. Making a game will make you understand the language better and challenge yourself as a programmer.
I'm not really too familiar with algorithms, specially those for games. Can you let me know what algorithms I should go and learn? Also, XNA is no longer supported by Microsoft, so should I just familiarize myself with Unity3D since it also supports C#?
Most of the algorithms you create for (ie: game mechanics) are defined by you. They are not different from what you have been doing in general programming. What you should learn about is data structures and how they work and apply them to your game. Sure, you can use Unity. It is your preference. Play around with it is my best advice for learning game programming.