Kodi stores the watched status in the database and it is linked to an absolute file path. If you backup and restore such that you are copying the databases and sources and on the new box the file paths are the same, or alternatively tweaked with path substitution, your watched status will be preserved.
Other options for preserving watched status would include using an add-on such as Trakt to store this information outside of Kodi, or exporting Kodi’s library to individual files which will save the metadata including watched status in files sitting next to your media. In this way if you scrape in the media anew on the same box or another the watched status can be imported from those saved locations.