The word in this sense dates back only to the 1960s in print and probably the immediate post-war years in speech. It is a multiple bet involving doubles, trebles and an accumulator rather than anything straightforward such as a win single.
Accordingly, I'd guess it relates to the American tendency in those days always to claim the biggest , best and most wonderful of everything...in other words to go over the top. Some British gambler or bookie probably thought calling the complex bet a Yankee gave expression to that penchant, suggesting that only an American - originally - would try such a thing.