Anyone with a rooted Fire OS 5 device, including the 1st and 2nd-gen Fire TV boxes and the 1st and 2nd-gen Fire TV Sticks, can now update to software version 220.127.116.11. Rbox is still at it after all these years and has just uploaded the newest images to flash. You can find them at the top of these XDA threads: Fire TV 1 (Bueller), Fire TV 2 (Sloane), Fire TV Stick 1 (Montoya), and Fire TV Stick 2 (Tank). If you have the means, please consider donating to Rbox to show your appreciation and to keep future updates coming.
Remember, your device has to already be rooted in order to install these pre-rooted images. These files will not help you root your device. They are simply already rooted versions of the stock software update, so people with rooted devices can update their device without losing root access.
Updating my Fire TV rooting guide and catching up on all the rooting/unlocking/flashing advancements that have been made during the last year is near the top of my todo list, so I hope to write some posts and guides related to that soon. Let me know in the comments if there is anything specific that you want me to cover.