Why is the input pin to my multiplexer considered a capacitive load?
Your mux is CMOS; MOS gates have capacitance [by design]... and a lot of other parasitic ones. But even with BJTs you have parasitic capacitance.

Here's what CMOS analog switch (as would be used in a multiplexer) typically looks like



Image from this book.

Every MOSFET has [parasitic] capacitance between everything and everything basically, so there is a capacitive path from an analog input to... well anything. I'm not actually sure relative to what you've measured it (output, ground?), but doesn't really matter, because some capacitance exists relative to any of these. 



In particular all MOSFETs in a CMOS will have capacitance via the bulk substrate:



Someone more versed than me in IC design can probably guess how you've measured it based on the result you've got.