Many, many thanks for this crucial info!
I installed the two Gen10 servers at the beginning of January and for some reason I have not been offered an HPE ESXi 6.0 U3 image under My VMware. That's why I used the HPE ESXi 6.0 U2 image and then upgraded the ESXi servers via VUM. Exactly here was the mistake, it must be a U3 image.
Today I just did an update installation with a current U3 image (VMware-ESXi-6.0.0-Update3-6921384-HPE-600.10.2.0.23-Feb2018) and now the keyboard input works in the Remote Console.
regards
Alex