SATA 3 is meaningless to mechanical hard drives. Even 10,000RPM Velociraptors can not move enough data to saturate SATA 2 (3Gb/s ) completely much less SATA 3 ( 6Gb/s ). The faster SATA 3 is used by SSDs only.
Since it's cheaper to make a commom interface for everything newer hard drives have a SATA 3 interface. Meaning the link is capable of moving the information even though the drive is not. This is just marketing hype that makes all the people who don't know better think they are getting something they are not.
Even if the hard drive was slow the only way it would affect game performance would be in level load times. A slow hard drive would not make you get fewer FPS or anything.