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Tulane University professor Rosanne Adderly says:

[T]he phrase "West Indies" distinguished the territories encountered by Columbus or and claimed by Spain from discovery claims by other powers in [Asia's] "East Indies"... The term "West Indies" was eventually used by all European nations to describe their own acquired territories in the Americas... considering British Caribbean colonies collectively as the "West Indies" had its greatest political importance in the 1950s with the movement to create a federation of those colonies that could ultimately become an independent nation... Despite the collapse of the Federation [in the early 1960s]... the West Indies continues to field a joint cricket team for international competition.^[5]

Despite the clarification that they are not actually part of India, the term stuck, primarily for British imperialistic reasons.

The West Indies cricket team includes participants from Guyana, which is geographically located in South America.