Yes they can, just like an archery ranger can use it for both.
All rangers can two weapon fight, because all classes can use two weapons. Rangers just have powers that specifically need two weapons to use such as twin strike.
The benefit of the two weapon fighting ranger is that he gets toughness and allowed to use one handed weapons in his off hand as if they were off hand.
The archery ranger gets defensive mobility. I really think prime shot should have been archery style only to help beef up this choice.
So the archer can pick up his longsword and shortsword and use Twin strike with melee weapons, but the two weapon ranger can do it with two longswords.
Nothing stops the archery guy from doing both, except typically the melee focused one has a stronger str than dex and the archery one has a stronger dex than str. Both can use which version of the power they want depending on the situation. Otherwise the archery character would be very weak compared to the melee ranger if left at close range.
The styles are just there to provide a little flavor and help you decide what attacks to focus on.