The Fire TV Stick has been rooted by directly interfacing with the device’s 8GB eMMC storage chip. This is a hardware root that involves soldering leads to specific points on the Fire TV Stick’s circuit board; not a software root like we had with towelroot on the original Amazon Fire TV. Due to the complexity and skill involved, it is unlikely that many people will replicate this rooting procedure.
The guys over at GTVHacker have posted details about this rooting method and a video demonstrating the procedure. The process involves soldering connections between the Fire TV Sticks 8GB eMMC storage chip and an SD sniffer board. This then allows you to mount the Fire TV Stick’s file system on a computer using a standard SD card reader. Once the file system is directly accessible via the SD card reader, you simply copy an SU binary file to the Fire TV Stick file system and set the appropriate permissions.
As I already mentioned, most people won’t be attempting to reproduce this method. However, achieving root in any form is great news as it may lead to a software root being discovered.