YouTube 2 Player by Rasmus Riiner

Legacy version
For pre-Quantum Firefox or Pale Moon, the legacy version can be found here:
https://github.com/sumzary/yt2p/releases/tag/v2.1.1

Setting up
After FF57, an additional Native Client is required.
Download yt2p-nativeapp.zip and follow instructions here:
https://github.com/sumzary/yt2p/releases/latest

Configuring players
Open the add-on settings.
Players are sorted into groups. Pick the active group on the left itembox, then the active player on the right itembox. Below the boxes are the Name, Icon, and Command input fields for the active item. Command is the most important, requiring the player executable path and URL identifier.

"C:/Program Files (x86)/mpv/mpv.exe" VIDEOURL
Opens a video in mpv player. Notice the quotes around the file path.

"C:/Program Files/youtube-dl.exe" -f 22 VIDOURL
Downloads a 720p video. Change the exe path to the actual youtube-dl.exe file.

youtube-dl --format 140 --extract-audio --audio-format mp3 VIDEOID
Downloads a mp3, "140" is a audio-only format on YouTube, more info here:
https://github.com/rg3/youtube-dl/blob/master/README.md

LINKURL - becomes the raw right-clicked link url,
VIDEOURL - is the same, but standardized, if it's a YouTube video url.
VIDEOID - is the extracted video ID.

Why bother?
It'll probably run smoother, you can make use of the player's filters, change the aspect ratio, maybe save the video for later... it's just what a professional ought to do.

mpv
The best player I've found.
https://mpv.io/

youtube-dl
Download videos in any format you'd like, including audio-only.
https://rg3.github.io/youtube-dl/

Media Player Classic BE
A light-weight player based on the original MPC and the MPC-HC projects.
https://sourceforge.net/projects/mpcbe/

DAUM Potplayer
https://potplayer.daum.net/

VLC Media Player
http://www.videolan.org/vlc/

BS Player
http://bsplayer.com/

Notes
This add-on is no longer under active development. If this add-on feels convoluted, it is. It's frustrating having to use the native messaging API for something as elementary as running an executable, a no-brainer before Quantum. Development shall continue once Mozilla has provided an alternative API.
Thank you for your interest in YT2P.