Thank you for the feedback. I will try the addon on some different devices of my friends and try to find out what the problem is..
Just to be sure, did you try it out on a website other than '*.mozilla.org'? It is blocked on Mozilla websites, can't do anything about IT.

I am sorry to hear that. I guess you have latest versions of Firefox and the plugin installed? I have two ideas what might help:
1. Open 'about:addons' and select the Mobile Gestures addon. Then check, if all input fields are filled. Usually it should be prefilled, but if not, you can define your own gestures as described in the addon description. When fields are filled, hit the save button.
2. Maybe you just used too less of your screen for the gestures and just try to move your finger (one at a time!) further in each direction (e.g. about three quarter of the screen horizontal)
Hope this helps! :)

Thank you for the positive feedback! That is a great idea. I am gonna try to add such a page in the feature.

Update 07. June '18: As you said it was pretty easy to change the addon. In the latest version 1.2.3 you can customize the gestures. The settings page can be openend with the guesture Down-Right-Up-Left or when you open 'about:addons' and then select 'Mobile Gestures'. There you can use D for Down, U for Up, R for Right and L for Left. Right now there is no input checking. But this will be added as well.