If it's not Ex, Su, Ps or Sp, it's Natural. Movement modes are natural unless specified otherwise. Natural attacks are natural. Other nonmagical functions of the body are either Extraordinary or Natural. Since body shape isn't specified as Extraordinary, and is nonmagical, then yes, it is a Natural ability, as noted in my quote from the SRD.
And yes, ability scores are Natural abilities as well, but 'ability score' is far and away not the only kind of ability that exists. After all, Su, Sp, Ps, and Ex abilities are also abilities, and ability scores are specifically called out as separate from 'racial abilities' as mentioned in the power.
So yes, that's exactly it. Arms, legs, neck, and other functions of body shape grant racial abilities, as noted by the fact that they don't fit into the categories of Su, Sp, Ps, or Ex.