Capsule toy machines are known as gashapon (or gachapon) in Japan. Unlike the ones you see in the US designed to catch parents and children walking out of a grocery store, the machines in Japan are bona fide destinations. They don’t just dispense five year-old gumballs or cheap plastic trinkets, they dispense high quality collectors items (similar to what you might find in a “blind box” or “blind bag” in the US) that sometimes sell for much more than the $1.00-$5.00 you paid for them.
You’ll see entire stores of them while you walk down the street, especially in shopping districts. The word gashapon is onomotopoeia—”gasha” refers to the sound when you turn a crank, and “pon” refers to the sound of the capsule dropping. Gashapon was introduced to Japan in the 1960s by Bandai (who still owns the trademark to the name), but multiple manufacturers make them these days.
There are actually a number of Gashopan models and replicas available for purchase. This 1/12th scale capsule toy machine is the spitting image of the one in the game. It's tiny, it requires assembly, and it doesn't actually function, but it's a neat little model kit.