Can I get into the gaming industry as solely a writer?

It's possible, but extremely difficult, as there are few positions and they are extremely contested. It helps to have published work in other mediums to build a portfolio.

Story is often created by designers working in tandem with the writers, art, and cinematics teams, so I wouldn't rule out pursuing technical skills. You'll have more opportunities available to you.

I'll second what Brendan said. Most of the "game writers" I know continue to write in other formats (novels, films, etc.) just like composers make music for games and movies or voice actors do games and cartoons. Unless you are at Blizzard working on World of Warcraft, a studio can't afford to keep a writer in-house just writing stuff. You'll usually be a contractor writing for a specific period of time or on a specific game and then the contract is up. So most writers are working on multiple projects simultaneously or at least chaining them together to maintain some sort of income.

As for the technical side, the more you know the more useful you are. Whatever you write has to get into the game somehow. If the programmers can hand you a tool that lets you enter the quest dialogue yourself, that frees them up to do something only they can do. I don't know about you, but as a writer, I don't trust other people with my words. Whenever possible, I'd rather have direct access myself to make edits or additions. Now I'm not talking full-blown programming, but you should be comfortable with production tools and markup languages like HTML or XML. Being able to maintain all your dialogue lines in Excel is a good skill to have, too.