Here is how,
Killing empowerment is a power that you become stronger and faster by killing. You can also gain new powers and so on.
But there's more than just that.
Oryx's taken power is absolute will, to implant your will into someone else.
[spoiler]Users become stronger, faster, more durable, etc. by killing others, possibly unlocking abilities related to the affinity and enhancing the existing powers. Some users may be able draw sustenance from the kills or even slow or stop aging.[/spoiler]
Reference:
https://youtu.be/ScWgznmtR4Y
https://www.bungie.net/en/Forum/Post/183949271/0/0/1
Killing empowerment was a concept before sword logic.
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It's more than that. Sword logic. Knowledge is power. Power is pain. Pain is life. Is the fundamental of sword logic. Killing proves you're right to exist over what you killed and proving your existence to be powerful brings knowledge of the secrets of the deep. Which in turn grants more power. Which needs more pain giving and taking life.. ad infinitum Oryx is more than a master of will he's a master of shapes reshaping things to his will. Planets, being, realities, all things shapable given sufficient power.