It turns out that installing nvidia-xconfig and creating an xorg.conf file with Option "DPMS" "true" in the "Monitor" section makes the screen turn off as desired.
The nvidia-xconfig package description says that "This tool is deprecated. The NVIDIA drivers now automatically integrate with the Xorg Xserver configuration. Creating an xorg.conf is no longer needed for normal setups." This leaves the questions: What exactly is that "Xorg Xserver configuration"? In any case: DPMS should be part of any "normal setup".
