Reading Table 2, 3, and 4 describe the hardware of the Fusercore, BMI160 (accel) and BMI160 (Gyroscope) inside the package. The FuserCore draws 800uA when active, but there is no power mode where the core is always active. The same goes fo the accelerometer, it samples data at 1600Hz, but there are no power mode when you can get 1600Hz data continuously.
You could however replace the code running on the fusercore to fill up the BMI160 1KB FIFO with 1600Hz data, then empty it and process it, but the CPU does not run fast enough to do this in real time, so you would end up with 1600Hz data periodically, but not continuously.
Hope that clarifies the sample rate question. If you do need fast raw data, the Sensor Hub does not offer you any value, what you need is the BMI160 standalone IMU.
You need to first upload firmware to the sensor hub, enable virtual sensors, then proceed to empty the FIFO using the protocol outlined in the sample code. BHI160 does not have data registers, only FIFO.