There is one important part missing. Machine certificate authentication required some changes on the gateway side that are not mentioned in the Client Admin Guide. The referenced SK (valid for EOL versions only) in the Client Admin Guide refers to some registry changes on the CLI which are not necessary as they are condfigured in SmoartConsole now. TAC pointed me into the right direction: https://sc1.checkpoint.com/documents/R81.10/WebAdminGuides/EN/CP_R81.10_RemoteAccessVPN_AdminGuide/T...
It is especially important to have the machine_certificate realm configured. I did this using GuiDBedit as described on step 6. It also requires a rule with an access role for the machines to get access the required ressources for domain login (DNS, AD, etc).
What I also noticed: the tunnel is disconnected as soon as the user entered his windows credentials and pressed the Enter button. There is no VPN connection until the user starts the VPN client and logs in there. Any logon scripts that are loaded after Windows logon will probably not even be fetched. A delay would be nice to allow such scripts to execute before the machine tunnel being disconnected.