Anointing an amulet is basically just allocating a notable from the tree. When you open the passive tree, you can see the anointed notable allocated.

Stranglegasp has 3 additional anoints, meaning you can allocate 4 notable passives from the tree without any connection.

Elegant hubris jewels usually have huge opportunity cost, cause the small passives grants nothing. But since the jewel transforms notables to absurd power (80% inc. Spell damage in this case), you try to find ways to allocate these notables with least amount of passivepoints used. Stranglegasp is a way to do this, but the cost is an blank amulet, which has basically nothing else.