No, SATA cable is not broken, it simply is not supplied with the product.
If you want to purchase one, you can do so through Micro Sata Cables (see here: https://www.microsatacables.com/intel%20nuc%20sata%2022%20pin%20sata%20drive%20fcc%20cable).
Now, I found that, with a standard double-wide graphics card (also) installed in the Ghost Canyon chassis, there is zero room to put a SATA HDD/SSD anywhere in the chassis.
BTW, for that USB header, you can also get the cable from Micro SATA Cables. Here is link: https://www.microsatacables.com/intel-nuc-nuc6i7kyk-skull-canyon-internal-usb-3.0-header-cable-skc-1105-usb3.