Awake-to-deceit:
I believe it signifies the trinity/occult, I don't know how long the term 'stylised atom' has been around, I'm pretty sure Borromean Rings pre-date this modern application and that they can have multiple forms of parametrization.
You're welcome to believe whatever you like, but there isn't some 'special' reference to the 'Trinity' (or the 'occult') every time there happens to be three of something. The three dots and rings represent the three electrons of a lithium atom and their associated orbits, as depicted in the Rutherford model.
"Stylised atom" is not a 'special term'. Stylised means what it means, and atom means what it means. Atoms are too small to actually see, so all depictions of atoms are technically stylised, but in this case it is stylised in a manner similar to many logos and other insignia to convey a concept in a non-technical manner. The lithium atom is frequently used to represent atoms in this way because it is more readily identifiable as an atom than simpler hydrogen (one ring) or helium (two rings) representations, without being unduly complex.
Borromean rings by definition are interlinked in such a way that all three rings are linked, but removing any one ring results in two remaining unlinked rings.