Many distros like Fedora and CentOS come with Flatpak pre-installed. If your distro does not support Flatpak out of the box check out the Flatpak Installation Guide.
In case this does not work - or you prefer the installation via command line:
cd Downloads/flatpak install ./BabelEdit-5.3.0.flatpakBabelEdit should automatically appear in your Applications list. Some systems might also require a restart.
You might see the following error during installation:
The application com.codeandweb.babeledit/x86_64/master requires the runtimeorg.freedesktop.Platform/x86_64/20.08 which was not found
If this is the case, the Flathub repo was not added to your system. It contains the base image, BabelEdit needs to run.
Open a command line and run:
flatpak remote-add --if-not-exists flathub https://flathub.org/repo/flathub.flatpakrepoflatpak install ./BabelEdit-5.3.0.flatpak