Firefox ver: 51.0.1 (32-bit)
ublock origin 1.10.6
I'm also experiencing the same. I've tried with only flashgot enabled but still the same result.
Two things I noticed.
1. Changing the resolution adds a new download option. The bolded text is the current video resolution.
2. The option to download (the flashgot button that appear) appears on the tab where you opened the link rather than on the tab where the video is. However, in youtube's case, it does appear but the option is sometimes limited (video download only).
The download option also appear when switching to a different tab or opening a new tab. This only happens with youtube (probably something to do with youtube's video algorithm). This doesn't happen with gfycat or twitch clips.