Did you maybe already have a different version of Tiled installed on your system? The installer only supports a single installation of Tiled per system, so you may be able to resolve your issues by going into "Add/Remove Software" and uninstalling all listed versions of Tiled, before trying again to install Tiled through the itch.io app. If the installer continues to fail for you, you could instead use the "snapshot" version, which is distributed as plain zip archive.
I'm working on maps for my wife's D&D campaign, and the houses I've sketched have diagonal walls, so when building the actual town, I'm having trouble finding tilesets with diagonal buildings/walls. Eventually I'll make my own tilesets, but I was hoping to get something quickly thrown together so we could get the adventure tested.