I think our translator is over-translating here. Nock simply has "all things in existence rejoice in likeness, and turn away from unlikeness," and I see nothing in the Greek that we should render in a reflexive or self-referential way as "like them."

So, initially this makes me simply think along the lines of "delighting in harmony, and being averse to discord."

There's a passage in the last section of Plato's Phaedo (109a) that uses the same term for "likeness" (or, as Taylor renders it, "similitude"). Here's Taylor's rendition of that passage. We're getting a report of the speech of Socrates:

I am persuaded, therefore (says he), in the first place, that if the earth is in the middle of the heavens, and is of a spherical figure, it has no occasion of air, nor of any other such-like necessity, to prevent it from falling: but that the perfect similitude of the heavens to themselves, and the equilibrity of the earth, are sufficient causes of its support. For that which is equally inclined, when places in the middle of a similar nature, cannot tend more or less to one part than another, but, subsisting on all sides similarly affected, it will remain free from all inclination.

Here, likeness/similitude is what's necessary (and all that's necessary) for the earth to maintain is equilibrium, rather than being pushed or pulled to one side or another.

Maybe this sheds some light on Sallustius' principle, too.