I saw this post the other day but I didn't get a chance to respond to it before because I was busy prepping for a programming interview at a video game developer today. :-)
what is the right direction to take to get into the video game industry?
If you're looking to do game programming, for even an entry level position you're either going to need some experience or a degree in Computer Science (or maybe CE). It wouldn't hurt to have a portfolio of impressive software projects that you worked on.
If you want to do game design, you will have a hard time getting hired without a portfolio of (good) games that you have worked on. Design positions are very competitive in general -- everyone has ideas and opinions, so you'd better have OMGWTF amazing ideas and/or a track record of making things that don't suck. I don't know how much a game design degree will help.
Other ways to try to get your foot in the door:
QA/Testing/Tech Support positions don't usually require specialty degrees. Some companies will promote from within if you prove yourself. Or you could try to go to school part time while working and then apply to programming or design jobs elsewhere once you have a relevant degree and some industry experience.
Internships can be a way to get experience -- if they're available, and you can get accepted, and you can afford to work for little or no pay for a while.
IT is another whole career path you could consider, although it tends to require its own training/certification/specializations. Maybe a little less sexy, but somebody's got to run all those servers and datacenters.
Computer science vs. Computer Engineering vs. ?
Again, if you want to do programming specifically you probably want a degree in CS. CE tends to focus more on hardware, although this varies depending on the school. If you're interested in things like working on game console hardware then a CE degree could be the way to go, but that quickly becomes a very specialized field.
What are courses I def need to take?
Game programming really involves everything these days. You at least want the basics: Object-Oriented Programming, Algorithms and Data Structures, Networking, AI, Graphics, Systems/Operating Systems. Math, especially Discrete Mathematics (which usually includes some Probability) and Linear Algebra. Any Bachelor's program in CS should cover all of those even if it's not specific to game programming.
Games with a significant online component can also need stuff like Databases, Data Mining, and can run into the kinds of scalability issues that generally fall under the "High Performance Computing" umbrella. Some CS programs may have specific advanced courses in topics like game engines.
Go for Master's?
If you don't have an undergrad degree in CS, you probably couldn't get into a Master's program in CS without taking a bunch of undergrad prereqs first. Depending on the program (and exactly what you took getting your undergrad degree) you may just need a few additional courses to catch up, or you might be able to work towards both a Bachelor's and Master's degree simultaneously if you go back to school full time.
Entry level programming positions shouldn't require a Master's degree.