TPE-DEL is definately two segments. It is two different flight numbers. For example, it is CX401 TPE-HKG and CX753 HKG-DEL. The flight number for the TPE-HKG segment varies depending on the day (eg CX531, CX471 or CX401). The only way it can be one segment is if it is one flight number all the way through, and it is not.

The same thing for the JFK-HKG-TPE. This is two different flight numbers and hence two separate coupons required, therefore two segments.