He means using the “live boot” method - using a USB based install of the Linux OS and then writing HAOS to the NUC SSD.
If you install via the live boot method - then you will have HAOS running on the NUC.
If you run Ubuntu on the NUC and want HA running as well you are limited to Home Assistant Core and Home Assistant Container methods - both of which require a bit of fiddling and are definitely not user friendly.
If you insist on running Ubuntu I would recommend running HAOS in a VM.
All the above methods are described in the docs under the page you linked or under Linux installs.
My personal preference - if you have the hardware spare is to dedicate the NUC to HA using HAOS - more convenient, better performance and simpler to install, backup and restore.