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Devices such as that one arent intended to blow the hot air back into laptop cases, many laptops don't have vents on the underside. That device works as a conductor to cool the underside by blowing cool air onto it as well as conducting heat away as it acts as a large heatsink. That particular cooler may not be appropriate because it is wedge shaped to lean laptops towards the user.
There was a solution listed in some US based online stores for vertical standing Xboxes. It was a base with one or two fans inside, can't seem to google it up as I don't know the name of it lol. I think it works by blowing air in from the bottom so that the fans at the rear can exhaust the hot air as cooler air comes in.