The Throat corresponds in position to the throat centre of the classical chakra scheme, and it is the centre where the borrowing and the departure are both easy to see.
The correspondence
Both schemes place a centre at the throat and both associate it with expression and speech. That much is carried over. What Human Design adds is a structural role: in the bodygraph the throat is the point through which the other centres reach outward expression, and the type classification turns partly on which centres connect to it. That structural function is the system's own and has no counterpart in the classical model, which describes centres without connecting channels of this kind.
The arithmetic
The classical scheme most often cited in modern Western usage has seven centres; the bodygraph has nine. Two of the nine, the G or Identity centre and the Spleen, have no classical counterpart. The others correspond by position with varying closeness of function.
Both sides are moving targets
The sevenfold scheme is one arrangement among several described in Indian tantric traditions, and the version in general Western circulation is a popular settlement rather than an original. The comparison here is between a 1987 construction and that settlement.
Human Design was published by Ra Uru Hu in 1987. The atlas records it as a contemporary system.
Sources Rainbow Body: A History of the Western Chakra System from Blavatsky to BrennanKurt Leland with The Origins of Yoga and Tantra: Indic Religions to the Thirteenth CenturyGeoffrey Samuel, The Human Design SystemRa Uru Hu (Alan Robert Krakower)