They actually describe it as "6+1 degrees of freedom" [1] with the gripper being the "+1" - so it's got base, shoulder, elbow, wrist1, wrist2, wrist3, and gripper.

This is a conventional way of describing things. Traditionally robot arms come with a "tool flange" where you attach your own "end effector" (which might be a gripper, or a suction cup, or a welding gun, or a paint sprayer, or whatever) and we count the degrees of freedom before the tool flange separately from those after the tool flange.

Occasionally robots come with 7 degrees of freedom [2] which gives you more options for reaching the same tool flange position. This can be useful in certain applications, like working around obstacles in the environment. It's uncommon though.

[1] https://www.seeedstudio.com/reBot-Arm-B601-DM-Bundle.html [2] https://explicit-robotics.github.io/exp_robot/kuka_LBR_iiwa7...