You can only connect a USB device like this to a USB host. So that rules out a nano altogether unless you add a USB host shield.
Some types of Arduino are capable of acting as a USB host, like the Due. But then you will have to write the software that accepts whatever USB interface that touch screen presents. Not an easy task.
That touch screen is very expensive for what it is, I never understood why people think Amazon have good prices.
That data sheet is just for the big controller chip not the whole board. It does say there is an I2C interface on it but it is unclear if this is brought out on the board it is mounted on.
No library written for an Arduino will work with this board.