Fixing videos and music downloads on the new Youtube layout?
From time-to-time Youtube experiments with various layout changes to limited set of users, since you are here it seems this to be the case with you. Sadly, these experiments break downloading of music and videos by "Easy Youtube Video Downloader" and here are possible solutions to fix the issue.
The new layout seems to be the default theme for newer browsers now, I am working to fix downloads for the new layout and an update should get pushed in couple of days. Just keep the addon installed to receive auto-update. You can also try to switch-back to old layout for time-being using instructions provided below, you can always switch back to new from - https://www.youtube.com/new.
Try to open a video in PRIVATE MODE/Incognito Mode (Firefox Menu->New Private Window), this should load the REGULAR layout and you can see the "Download" button as expected. This will be a temporary solution to enable downloading once a while, you will continue to see the experimental BETA layout in non-private/non-incognito window of your web-browser.
To switch off the experimental interface and get back the regular layout (Recommended), click the Exit icon in lower right corner of youtube page to get back the old interface. On some tests you need to click the "three dots" icon before SIGN-IN link and click "Restore Classic Youtube", you should get back the old layout and the download button as shown below.