Can the length of a wire impact SPI transmission?
Yes, the length of the wires used for SPI can affect the functionality. Longer wires give more capacitance, which is harder to switch high and low at high data rates. But longer wires will still conduct current, and a continuity test is at low frequency, so something else is going on herre.

Try measuring the actual resistance of the connecting wires instead of using a continuity checker. It would also be helpful if you drew a schematic of how you are connecting the strips and exactly where you are measuring continuity. Also, the link you provided is the top-level link to the vendor, not to that specific product.