Do you know a Linux Desktop that doesn't implement the Desktop Entry Specification? I think all relevant ones do so.
The installer could still be optional.

TL;DR
A simple setup script should be provided in the factorio linux package so users can then simply start the game from the game menu.

What ?
A setup script could generate a Factorio.desktop file with the correct paths to icon and starting point.

It is usually placed in “ ~/.local/share ...

I have the same problem, so i just download the new archive and run my quick and dirty update-script.

#!/bin/sh

# Make shure you have the latest Factorio-Archive.
echo "Moving factorio to factorio_bak"
mv factorio factorio_bak

echo "Extracting Archive"
# The next line has to be edit each time ...