I think I figured out what Pyke REALLY is: nothing but a vessel for something far more dangerous...
So as he is set up, he's your typical spooky dead dude going crazy for revenge. At least that's what you are supposed to think, but some things do not add up, such as a lacking connection to the Shadow Isles, as any prim and proper undead would have, or his semi-material quality to change from mist to water to solid form like some sort of elemental.
However, now that it is past 4 AM, my brain somehow had a solution to this. He's not a dude, he's not a spirit, he's a the vessel of a STORY. A SENTINENT STORY.
As you see, Pyke operates without any sort of agenda or goal, he THINKS he's going for revenge, but by now literally everyone who was on that boat back then is long dead. His lore actually gave it away: it mentions some fictional ship, the "TERROR" that he hails from, even when there are no records of such a ship ever docking in Bilgewater. However, that's what he is: a "tale of terror". But he's not a demon or any sort of entity that would feed of that emotion, so why would he go out and kill people randomly?
My answer to that: A story wants to exist, because if no one hears it, it is worthless.
However, the story that now "exists" MUST NEVER END. Because a story that has ended is over, it does not cease to be, but is suddenly doesn’t do a thing anymore until it is actively invoked. If the story posesses sentience, it will do everything it can to prevent an ending. This is why Pyke is kinda in some sort of “infinite loop”, and his list never ends and always new names show up.
But at the same time, the story must not become mundane, it must not drown in the constant background noise that is the collective human subconscious - that's when it drives up the stakes. At first, it's just the Captains that he takes. Then the high officers. Then the crewmates. And then... literally everyone. To not fade escalation is necessary.
One should also note that the very founding principles of the creation of Runeterra are RUNES. World Runes. You know, like infinity stones, except they are not stones but words. Which means that the very core of existence is build on them. And in a world made of words, a story going rouge doesn’t seem so weird, now, doesn’t it?
Note that you could also replace "story" with "pattern" here. A self-sustaining, replicating pattern that imprints itself through knownledge of it. By some definition this would qualify as "life". Poor Pyke has probably no clue, the guy himself is merely a vessel, turned into a protagonist of a story he might have never chosen to take part in.
The only question left if this story was truly created by Pyke himself, a twisted manifestation of his dying wish taken form through magic, or if he is just a stand-in for a story FAR older, that wants to be feared again...