It's not about what rights Administrators can promote and demote. It's about the rights that are extended to the group. Discussion Moderators automatically have Chat Moderator rights. So it is useless to mention them individually.
On top of that, Administrators do have all the rights that Content Moderators have. They just can't grant and revoke them. That's a difference.
I think you are just a bit confused. Because the sentence in the help page clearly says "all the privileges", not "all the rights they can grant and revoke".
If you look at the 1st part. It mentions the abilities that Administrators have that are also included in the smaller groups. Chat Moderator rights are automatically covered by Discussion Moderator rights. While Rollback rights are automatically covered by Content Moderator rights.
Also in the 3rd part, the fact that Administrators can grant and revoke Chat Moderator and Discussion Moderator rights has already been covered. I hope that you now understand, now that I have formally explained it to you.
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