The name comes from an American game show. The mechanism is far older, and the mathematics behind it was described long before either.
Plinko appeared on the American programme The Price Is Right in 1983: a large vertical board of pegs down which contestants dropped flat discs, with cash values at the bottom. It became the show's best known segment, and the name attached itself to the format permanently.
Japanese pachinko parlours had been operating on the same principle since the 1920s: steel balls falling through a field of pins, with prizes decided by where they landed. Pachinko is mechanically far more elaborate, but the core is identical.
Both descend from a device the Victorian statistician Francis Galton built to demonstrate the binomial distribution: a board of pegs with beads poured through it, which pile up in a bell curve at the bottom every time. Galton's point was that a great many independent left-or-right decisions produce a predictable overall shape even though each individual path is unpredictable.
That is exactly the property online Plinko monetises. The shape is guaranteed; your path through it is not. The odds page works through the arithmetic.