Does Loop need WiFi to work?

No - you don't need WiFi but you do need an internet connection

The Loop Clip and Hub don't use WiFi to communicate, instead using their own frequency.  (If you're interested, they communicate over an 868MHz radio link which is a completely different radio frequency to that used by your WiFi network at home)

However, you will need a broadband router for your Loop Hub to send the data to the Loop Servers.

The Hub needs to be plugged in or alternatively you can use a spare USB port on your home router.