When the download seemed to be finished I tried to start the game. It then seems to have deleted the game contents anew and started the download again. This happens with all games I tried!

This is what it displayed after the second try
More system information: https://gist.github.com/Zamundaaa/8b64dd4af1608559850bee93fe271d3d
The game files seem to be in the downloading folder in my steam library. When I copied them into the gamefolder and started steam, I could start the game again. Still trying to verify the integrity of the game folder does result in a new download
Hello @Zamundaaa, it sounds like you are encountering #4800. Does the workaround at https://github.com/ValveSoftware/steam-for-linux/issues/4800#issuecomment-271763278 avoid the issue?
Even though the problem occurred on my machine even with small games (like 75MB), it does avoid the issue completely. Thanks
Your system information
Please describe your issue in as much detail as possible:
I had very strong network lags in Rocket League, just on my machine under Ubuntu, and not on my brother's machine on Windows. Because of this I thought I should validate the game files, so if some file were wrong and creating this issue, it would be downloaded again and replaced with a working version.
Steam then deleted the whole game and started to download it completely new. Neither my home folder, nor my steam library (which is on an external NTFS partition) are encrypted
Steps for reproducing this issue: