the game is more Twin Peaks than it is not, differing to the extent it contorts (and to an extent, misinterprets and plays loose with) the source material to lead up to a big nipponese boss battle
Be that as it may, that doesn't mean the game's writer ever saw Twin Peaks.
I'm a big fan of Twin Peaks and I like this game as well, but the writer of the game clearly didn't see the series. There's no understanding in the Twin Peaks references.
Someone did see Twin Peaks, for sure, and told the creator of Deadly Premonition about it and what we got was this. That's my best guess.
Like Twin Peaks through the game of telephone, sandwiched in between the usual nipponese crazy.