The Watched Words settings are currently only available to staff users, as Watched Words also contains other type of actions that are would typically be redistricted to moderators or admins, such as blocked or censored words.
I don’t believe there are currently any plans to change how the Watched Words settings are restricted to staff users, but if you think that a setting similar to the Watched Words Link actions would be a good addition to Discourse, please feel free to share any ideas you might have about this in our #feature category.