Saw this thread on Reddit...
https://www.reddit.com/r/leagueoflegends/comments/3bzey3/tahm_kench_originnature_possible_explanation/
Remember, this game is League of LEGENDS -and what "Lore" we have isnt encyclopedic its legend and LORE. It may not be accurate, and may have conflicting versions.
*When the Gambler hears the song that calls on him to chance his luck again -- A gambler, thinking the way out of his misery is by trying that last gamble.
*"The singer was a creature, with the biggest mouth the Gambler had ever seen (...)" -- Your thoughts become very persuasive when it comes to convincing you to indulge in your addiction.
So the Gambler ends up travelling away to try his chance again (sort of gambling isn't it?)
*"Now when that hungry beast finally did rise" -- When the Gambler's hunger for "dice and cards" (gambling) rouse.
*"And although the Gambler tried to cast him out" -- Although the Gambler tried to supress his own vices.
*"It ate the gifts, the house, and gold!" -- His gambling addiction ended up consuming everything.
*"This hunger's a burden, but it's the last time I swear, so please forgive" -- Now, are these the words of a demon/spirit? Or the Gambler's own words?
Basically I'm saying that Tahm is the materialisation of a person's own "demons", and Tahm will take the mannerisms of wichever person it wants to feed on.
He is the spirit of people's own, self made shackles.
Tahm let the Gambler try his luck again by going to some other land start fresh, but you can't run from yourself. Should the Gambler redeem himself it would have been wherever he was, with whatever problems he had caused. By trying his luck again he was letting the beast in - I think whenever the Gambler indulged, he let Tahm in.
Bits from the Q&A now,
Q: Tahm says that "the world is one river, and i'm its king. Ain't no place i can't go, aint no place i cant go again." Is this true? (...) And how does that work anyways? (...) Not every lake, river, ocean, pool and oasis is connected, (...) Maybe there is a massive underground ocean that only he knows of?
A: There is an ocean of darkness in every man's soul.
Q: In the River King video, Tahm makes a bargain with the gambler then comes to collect years later. Why does Tahm even need to make a Faustian deal in the first place instead of crashing any party whenever he wants? Is he bound by certain rules? Is that what he meant by being "let in"?
A: Yes. Traditionally there are always rules with demons and devils. The gambler is making a bargain (ultimately with himself). It is the bargain that allows Tahm to create the human misery he feeds on.
Q: Why does Tahm feel the need to trick people? He could easily walk up to a village and eat everybody, since he obviously isn't threatened by most beings. He said that when he devoured the gambler's wife, it left him satisfied. Does he have some sort of physiological disorder? Supposedly he feeds on "despair", but i'm pretty sure anybody getting eaten by a giant monster will be in despair.
A: If I can answer a question with a question. Who's despair is Tahm eating in the story? How is his bargain causing the maximum amount of sorrow?
His bargain gives hope to the Gambler, who thinks that he has been given a new chance -- He has not. He gambled his way out, and "a person is its own worst enemy". By raising the Gambler's hope, then watching it being destroyed by the Gambler himself Tahm created the most misery outta that.
Tahm didn't get fed off of the wife, he got fed on the Gambler's misery and failure in escaping his own conditioning.