I've tried uninstalling and reinstalling, but the download finishes instantly and no files are added. Seems like the update broke it. I've tried to install it on others computers : nothing's happened, no .exe to launch. It seems to be general when you read topics in steam's forum.
Steam version of Legends of the Alliance not working anymore
I have alerted the FFG devs.
The steam installation is now repaired. All works fine ! THX