It's quite a transition! The biggest difference in mindset is moving away from the business world's reliance on abstraction to one where you're focused much more on the particular hardware you're targeting and getting things to run within strict budgets of time and memory. Game programming is a lot more like embedded programming than it is like web programming -- you have to think about the exact memory footprint of everything and CPU time is at a huge premium.
This is even true of being an MMO server programmer, because a) the server has to answer to each client command within 80 milliseconds to feel responsive, and b) the bigger the footprint of the game on the server, the more hardware you have to buy, and that costs real money.
First up you should learn C++ if you haven't already. Almost every game is written in C or C++ these days. Game consoles have strictly limited memory, and if you allocate one byte past 512mb it doesn't slow down, it crashes; at the same time, each trip through the main app loop has to complete in 33ms or less, so we can't rely on garbage collection and smart pointers. The game-development world is one of those special applications where you really need to do all those optimizations that people here say you never need to do any more.
Also, bone up on your math. Games are built out of linear algebra and kinematics -- not just the graphics, but the state of the world and the behavior of every character and object. I like Eric Lengyel's book for game math; it's been my bible for years (though there are many other good ones).
You could try to learn some graphics math and programming as well, but this is sort of a subspecialty now and typically only a couple of people on a game team are really working at the level of DirectX calls. I suspect you're more interested in game logic and server backend, which is less specialized.
Make games. There are many frameworks to help you get started. XNA has the advantage of being a real-world product that actual games are shipped with, unlike PyGame or SDL which are quick to get up and running but have vanishingly little commercial support.
I would recommend having a look at Joe's Blog as well.
For math, have a look at this book.
The book "Computer Graphics: Principles and Practice" (known in the Computer Graphics circles as the "Foley-VanDam") is the basic for most computer graphics courses, and it covers the topic of implementing a ray-tracer in much detail. It is quite dated, but it's still the best, afaik, and the basic principles remain the same.
I also second the recommendation for Eric Lengyel's Mathematics for 3D Game Programming and Computer Graphics. It's not as thorough, but it's a wonderful review of the math basics you need for 3D programming, it has very useful summaries at the end of each chapter, and it's written in an approachable, not too scary way.
In addition, you'll probably want some OpenGL or DirectX basics. It's easier to start working with a 3D API, then learn the underlying maths than the opposite (in my opinion), but both options are possible. Just look for OpenGL on SO and you should find a couple of good references as well.