What is a "gin martini"? Martinis already have gin as their alcoholic base.
The word "gin" here is to distinguish the classic gin-based martini to the just-as-common vodka martini.
Martinis originated as gin and vermouth but later the term martini is just as commonly applied to vodka-based drinks, so simply stating "martini" now fails to distinguish, linguistically, whether the author is referring to gin- or vodka- based drinks.
martini http://dictionary.reference.com/browse/martini
[mahr-tee-nee]
noun, plural martinis.
1. a cocktail made with gin or vodka and dry vermouth, usually served with a green olive or a twist of lemon peel.
From various sites about drinking around the internet, such as http://cocktails.about.com/b/2008/03/22/vodka-or-gin-martini.htm:
"A martini is traditionally made with gin, and therefore if you are wanting its vodka containing cousin you should request a vodka martini. However such is the popularity of the vodka martini that if you order a martini at a bar, many bartenders will now ask whether you would like vodka or gin. Many people think the vodka martini came first and would be surprised to learn that it was superseded by gin. Whilst Gin is making quite the revival at the moment, I think that the vodka martini will still be outselling the traditional martini overall."
"When I was a bartender, I'd say about 90% of martini drinkers order vodka martinis. It's become so popular that most flavored martinis are made with vodka as well"
"Today, the Vodka Martini is as popular as the classic Gin Martini which it was adapted from. It is the drink of choice for many who want a clean, dry Martini without the aromatic botanicals of gin and, just as with its predecessor, can be adapted to suit the drinker's personal taste."