stopover back in the same region - still eligible for 72-hour visa-free?

i'm a US passport-holder. my ticket is

hong kong to shanghai
SH to taipei

but my SH to taipei has a stopover in hong kong, and when i called my airline, they said that in SH, they will issue me a ticket to hong kong. in that case, it just looks like a hk-SH-hk round-way trip.

is it the case that i'm not eligible for the 72-hour visa-free transit, even though in reality i'm going hk-SH-taipei?