TinyXP has many features removed, one of which is the removal of 16bit support. winnt.exe needs more than just itself to run, you will need to install a proper version of XP for this method to work.
Windows XP can be installed, then using the add/remove applications you can remove all of the unnecessary parts.
There is also the option of creating your own custom XP installation with the application nLite. I use this for my old laptop (12GB of space) to remove all the stuff I don't want, but making sure to keep the 16bit essentials.
It can be downloaded free: nLite - Deployment Tool for the bootable Unattended Windows installation