the original client is here https://github.com/bitcoin/bitcoin
the original client is here https://github.com/bitcoin/bitcoin
It is true that BCC will be a continuation of the original chain, and it is also true that in some substantial sense bitcoin cash can be said to be a continuation of the original bitcoin blockchain and incentive model to a greater degree than bitcoin core will soon be, as bitcoin core moves over to segregated witness with a "block weight cap" rather than "block size cap".
I therefore rate MichaelBurge's sentence "BCC is not actually a fork but is the original chain/software, isn't it?" as false (it is a fork), true (it is a continuation of the original chain), and true (it is a continuation of the original software).
Or are the Segwit chains completely irrelevant here?
No, segwit is an optional backwards compatible protocol extension that people can choose to use... not a fork. You can bridge an original bitcoin node onto the network using segwit and modulo segwit unrelated software bugs that just make it get stuck, it will reach consensus with the network fine.