A 'major', in educational terms, is your focus during college. Someone who's an economics major takes a lot of classes on economics during college, and earns a degree such as 'Bachelor of Arts in Economics'. (Arts is a very loose term in education - it has nothing to do with painting in this case
).
There are a small number of jobs that are easier for gaijins to get. Most of these involve...
1. Teaching (English, or other languages)
2. Translation (this is where I'm hoping to end up)
3. International relations (can either be on a business or government level)
I know a fellow who worked for Square-Enix by the name of Richard Honeywood. He was the head of the localization department, and he was responsible for translating several of the Final Fantasy games into English. So it's not impossible for someone who loves games to work for a Japanese gaming company. Personally, it's a job I'd quite like to shoot for myself one day, but they are probably small in number -- there are a lot more translating jobs in areas such as business and legal firms.