Upvote:3
For those that haven't see it, I presume what you're referring to is Heineken's Departure Roulette, which whilst a cute concept is really nothing more than advertising.
Over the years some airlines have run "mystery" fares where you would turn up at the airport in the morning, and fly to a (seemingly) random location for the day for a relatively cheap fare. However I haven't seen any such promotions for many years.
The nearest you'll probably find are the close-in fares that some airlines offer on a regular basic, such as United Airlines's Weekly Specials which go up on Monday/Tuesday for travel over the following weekend. The destinations vary week to week depending on how full the flights are.
Otherwise you can use services such as Kayak Explore to keep an eye out for cheap destinations in the near future - although unfortunately Kayak Explorer doesn't allow you to select a specific date, only a month range.