I have a portfolio that ranges everything from the story treatments I have written for major production companies to essays I have written in school (and gotten an A+ on, of course
). If you are trying to get a job writing dialogue or whatever, then the more creative the samples, the better.
I remember BioWare was hiring an assistant writer not to long ago, and they had a specific format that they wanted for a portfolio submission; they even gave you a sample template to use! Each company is different in what they look for. The more prestigious the company, the more they look for, and the harder the competition will be.
Search for the game dialogue template that's floating around the internet and use that to create a dialogue scene between a player and a NPC. Do different styles, from medieval to sci-fi.
As far as what skills I am trying to develop, I can't program, can't draw, so I am forced to either enter the industry using my filmmaking/screenwriting skills, work my way as a producer, or enter as a QA tester and work up from there (which seems to be the most realistic).
To be honest, I may still pursue a screenwriting career, I am really not sure what industry I want to get into. But, that's another story.