It's called tortious interference with contract and the standards vary state by state. However, the common elements are (1) the existence of a contract subject to interference; (2) the occurrence of an act of interference that was willful and intentional; (3) the act was a proximate cause of the claimant's damage; and (4) actual damage or loss occurred.

Some states also recognize causes of action for interference with prospective relationships, although these are notoriously hard to prove.

What contract? All I see is the same clickwrap you violate when you jailbreak your device and install f.lux the old fashioned way.

This is an end-run around Apple's policies, just like jailbreaking. Apple doesn't like it, just like jailbreaking. The only hard to understand or confusing part is where the f.lux developers deicde they suddenly care enough about what Apple does or doesn't like to pull their app.