The reason is that Serial.print() is mush slower compared to reading a sample from the sensor.
If you comment the print(), then read sensor data for a certain time repeatedly and calculate the output data rate accordingly, you will find that the sampling rate is indeed 1000 Hz.
If what you wanted is merely to store the data and use it afterwards (instead of real-time processing), you can store the sensor readings in a SD card, which is always much faster than serial printing. A useful trick is that do not write data to the sd card whenever you get a new sample, but use a software buffer (i.e., array) to store the samples (the buffer size depends on the RAM of microcontroller) and then write the whole buffer to the sd card when it's full.
However, as long as you want to store the data (either print in serial or write in a file), you'll always have to 'sacrifice' some data rate and cannot get 1kHz as mentioned in datasheet. Hope this helps.