I really don't think spending a decade 'traveling' is going to do all that much for your writing skills.
10 years is a big chunk of your life to be making mediocre wages in a country where you have half an understanding of the language, if that. One year? Sure. 10 years? No way.
He means life experience. Writers draw a lot on life experience. The more life experience the better. Robert Ludlum, author of 25 New York Times Best Selling novels, never wrote about a location in his novel unless he traveled there first. It just makes it more authentic. Life experience allows me to channel feelings, emotions, pain that is tucked away in my heart and pour it onto a page. This allows a better connection with the reader. I hear so many people joke about Bioware feeding on the tears of players. To be honest, if one of Bioware's games makes an emtional impact to you, the player, you have no idea how happy that makes the kind folks at Bioware. It means they are writing powerful stuff to put it in layman's terms.
However, a degree in psychology means nothing...unless you want to write nothing but psychological thrillers (p.s. I love psychology and have a lot of friends with psychology degrees btw). If you want to write fantasy, I recommend history. Do you like superheroes? Try mythology. Science fiction? Be a science major. 50% of a writer's job is research, research, research. To me that's one of the best parts.

But yea, life experience is vital. I studied professional writing and film after I got an Associates in business. I did screenplay writing, directing, and film editing at film school. Did some cool work in the indie film scene before I grew bored and made a change in my major. However, my time in film school is where I got a lot of insight into the video game industry. Even more so than my time as a game journalist. The film industry and video game industry are pretty similar in function (someone from Bioware can feel free to correct me if I am wrong).
Professional Writing was awesome. They cover everything from journalism, business and legal writing to short stories, poetry, film, comics, and novels. As for writing for a video game studio...the best way to do that is write novels. Personally, I would be floored at the opportunity to write for Bioware...or DC Comics...or Marvel. Haha. However, the best way to get their attention is by getting yourself out there and get published. Show you can craft a good story. That you have what it takes to get published. And don't do self publishing. That's just a warning to you...
Oh and some night classes on writing will very likely NOT teach you proper writing mechanics. They may teach you basic storytelling principals, but I highly advise a degree in English or its equivalent. And I know this message is all over the place...making dinner while writing...potato soup it is fantastic...but I know what it is like to work in retail. I know how tough it can be. Don't give up writing. It takes discipline. Lots and lots of discipline. Don't give up. I've been there. Worked at places like JC Penney, Walmart, Macys, etc. Wasn't fun. Made little to nothing. But don't give up hope. Keep writing and you'll be surprised at the opportunities that open up for you.