That would be something akin to a false grip, where the thumb is not part of the grip it's self. Usually the bar is resting more on the heel of the hand, with the thumb behind the bar, with a true false grip. With the bar held this way,a more direct line of force/power is gained because the heel, wrist and forearm are inline. Also seems to be easier on the wrist. Some call these a negative grip, for whatever reason.
PL'ers and other heavy benchers will use this method now and than. Caution should be taken because that bar can slip or become out of control at times. Best to have a GOOD spotter at hand. or do benches in a PR, for your own safety. Might want to stickum or something like that when doing these.
Some use a false grip on curls or chins. Some guy's swear by this method. Can really be used on most exercises, though in my view only, I do not see the big advantage. BP'ing and overhead pressing being the exceptions. Seem to generate more direct power to these lifts. Good Luck.