That thing is an abomination, should never see the light of day and it cannot possibly be legal. Think about it for a minute; what happens if 1 of the 120V cord ends gets unplugged when the machine is turned on? That's right, you will have a 120V live prong exposed & waiting to zap someone because it's getting back fed from the other circuit through the machine. Even if the motor is not running but the machine has electronic controls that are in the circuit it can be enough to deal a fatal shock.
I hate to even think of the trouble you would be in if you brought that on to a job site & someone got hurt.
It would be possible to build such a thing with protection relays in it to disconnect everything if one of the sources is disconnected, but the website doesn't make any references to that.