Yes, they were correctly tagged as highways. You may be conflating the legal concept of a highway with the OpenStreetMap highway=* object tag.

As these highways exist and are visible on the aerial imagery, the correct approach is to add the access=private tag, not to delete them from the map.

Please read the following wiki articles before you proceed further:
https://wiki.openstreetmap.org/wiki/Why_we_won%27t_delete_roads_on_private_property
https://wiki.openstreetmap.org/wiki/Why_can%27t_I_delete_this_trail%3F

Some of these track are also shown on OS OpenMap Local, which does not provide for marking them as private access. There is absolutely no prospect of you convincing OS to delete these.

Reverted in https://www.openstreetmap.org/changeset/152234116