Solution
Not all USB chassis have both ground connections, in this specific case, the USB-6225 does. Both Ground Lug Screw and Chassis Ground Lug should be connected together and provide the reference point for the AI GND.
You can either ground the USB-62xx using the Ground Lug Screw or using the Chassis Ground Lug. How to ground the chassis using both methods can be found in the M Series User Manual at the end of page number 19.
NI-62xx devices and modules provide no isolation (check the fourth statement of the previous link), therefore the chassis ground is also the reference point for AI GND and the others.
It is necessary to provide this connection to the device because the power supply connected to the USB device only provides positive and negative connections. Additionally, for EMC compliance, the chassis of the USB M Series device must be connected to earth ground through the chassis ground.