This problem has been reproduced on Linux and on MacOS.

Setting the following key in server.cfg to allow only administrators to connect to the physical desktop:

PhysicalDesktopAccess administrator

doesn't grant access to system administrators. It works properly instead for NoMachine administrators.

As a workaround, add NoMachine administrator's privileges to the system admin:

sudo /etc/NX/nxserver --useradd sys_admin_name --administrator yes