Same issue. Thing is it works on another login on the same computer. Comparing both logs it looks like the base directory needs to be /Applications/Epic Games Launcher.app/Contents/UE4/EpicGamesLauncher/Binaries/Mac/
Both you and I have /Applications/Epic Games Launcher.app/Contents/UE4/Engine/Binaries/Mac/ as the base dir. I haven’t found a way to change it when starting the launcher.