Virtual reality head-mounted displays (VR HMDs) have become a popular platform for gaming. However, simulator sickness (SS) is still an impediment to VR's wider adoption, particularly in gaming. It can induce strong discomfort and impair players' immersion, performance, and enjoyment. Researchers have explored techniques to mitigate SS. While these techniques have been shown to help lessen SS, they may not be applicable to games because they cannot be easily integrated into various types of games without impacting gameplay, immersion, and performance. In this research, we introduce a new SS mitigation technique, VRCockpit. VRCockpit is a visual technique that surrounds the player with four 2D views, one for each cardinal direction, that show 2D copies of the areas of the 3D environment around the player. To study its effectiveness, we conducted two different experiments, one with a car racing game, followed by a first-person shooter game. Our results show that VRCockpit has the potential to mitigate SS and still allows players to have the same level of immersion and gameplay performance.