It is most likely that 16.04 LTS Does not support Appimage
Upgrade to a version of Ubuntu that supports the .Appimage file.
Here are the versions of Ubuntu that support Appimages:
Ubuntu 17.04 (Zesty Zapus)
Download to Ubuntu 17.10:
then after going to the link, click "Ubuntu Desktop"
then scroll down until you see a text saying "Ubuntu 17.10 LTS)
Click the download button. then when it is installed, you have to burn it to a USB Disk. if you don’t have a USB. Buy one online on www.ebay.com, if you have a USB already, Run Startup Disk Creator, then click the iso file that has ubuntu 17.10 on it. Restart the Computer, then hold or press F12 Or Enter, on most computers: F12
On some computers: Enter
Then boot from the USB. Now set up how to install Ubuntu.
Account name: Denis is Awesome
Install updates while installing Ubuntu has to be selected to upgrade settings of the new version
You can install Chromium and Flash.
That is the only option in the world!
Ubuntu 18.04 (Bionic Beaver)
and last but not least: Ubuntu 17.10!
that is the only option to get an appimage that is executable.
if that does not work, Im Sorry.