While it is extremely hard to make a living writing about video games and video game reviews, it is possible to make money writing video game reviews and this article will tell you how.
Write the video game or system reviews. These could be individual articles (like a review of Fable II), or comparative (why Oblivion still kicks Fable II's a**, for example). Be creative. The larger the variety of reviews you have, the more likely you are to make money selling those video game reviews.
Look at uploading those articles to Constant Content. You can set your prices and choose which rights to sell. Want credit? Sell only the usage rights. Want the money? Sell full rights for $30 more. This is a good marketplace for reviews, particularly for new video games, and I've sold several video game reviews from here.
After the article is accepted, rewrite the review and sell it to Associated Content for an up front payment, as well as a PPV (pay per views) bonus. This won't make you a lot of money, but it will begin a small stream, and I've received a lot of work from people who first saw my articles on AC - so this could lead to something better.
If you have a Squidoo and Hubpages account, you can make more detailed web pages on the games and/or systems you're reviewing, and offer products for sale as an affiliate, links to your AC articles or blog, and you can profit this way, as well.
If you know a lot about SEO and Internet Marketing, consider making your own web page/blog and putting your reviews on there with Adsense and affiliate links. While this could potentially make you a lot of money writing video game reviews, you really need to be good at Internet Marketing, SEO, and understand that this will take a lot of work and time to really pay off, but it can be lucrative and this step goes very well with the Squidoo lenses and Hubpages hubs.
Read print magazines based around video games, and figure out which sections are open to freelance writers. Submit your articles accordingly.
Single game video game reviews of new games work best on CC and AC. Comparison or list articles also do very well online.
Don't expect overnight success or a full time living writing video game reviews. It takes time, and is a crowded niche.