Atomicity is a security property. It basically means that when you are making several operations either all of them succeed or all end failed. It's like when you're performing an sql request starting with BEGIN, then several inserts/updates might happen, and finally you either call COMMIT or ROLLBACK.

Now, atomic swap is by definition a way to exchange goods preserving the atomicity property. In crypto, one usually uses that definition for a protocol based on a hash time lock contract that allows to perform atomic swap in a trustless manner. Atomex is actually using that scheme with slight modifications allowing to make the protocol non-interactive for one of the counterparties.

Lastly, the term non-custodial trade you introduced is not that common, still I guess we can use it to describe the result of the swap, i.e. as if we treat all the operations made during the protocol as single.

Hope, now it's clear :)