I was able to insert the Content Note through Workbench and when I queried it shows all the fields but not the Parent ID Field which means that we can't associate it with any Record via API or Dataloader.
Here is the screenshot of the workbench:
But this is having the Properties to share with People, Group when you open the record of Content Note.
But when I created a new Note from the Related List of Contact object through UI and queried from workbench still it doesn't show any ParentID field.
But when I opened the record from the Contact Object related List It is showing the ParentID in the URL. PFA
I don't think so that there is way to associate the Content Note with the any Object through DataLoader or API.