Unfortunately, as there is no benchmark capability built into the game (like their tech demos), I do not have any specific Linux hardware recommendations for OilRush. Simply put though, if your system can handle Unigine Tropics or Unigine Heaven tech demos, it should be able to run OilRush. This real-time strategy game's engine has been further optimized and tuned for greater performance.
Even if you're not the biggest Linux gamer or a real-time strategy fan, I still would recommend picking up this $20 USD Linux-native title on the basis of supporting Unigine Corp as one of the leading Linux-friendly commercial game studios. Unigine Corp continues to be very friendly towards Linux in ensuring their renderer and the entire engine run well on Linux, has given out free engine copies to Linux-friendly indie game developers, the game is free of DRM restrictions, their engine is the most visually impressive Linux game engine available to the public at the moment, they continue to put out free new tech demos / benchmarks (Unigine Valley is coming soon, Heaven will also be updated), and they do other good Linux deeds.