I activated the option to notify if an update is available. When I now select the update function, LibreElec downloads the latest GZ image and stores it in the update folder. After downloading and unzipping the system reboots. However after the first restart it doesn't update the system images. Instead I got the message again that a new version is available for download.
I tested it only on the Intel NUC machine which has "LibreELEC-Generic.x86_64-6.90.002.tar" installed.
I presume the "problem" is that the GZ image is being downloaded but during the update procedure at start up LibreElec check's if a TAR file is present (like it was the case with OpenElec).