Why is the text stretched out like that?

It is not letter-spacing at all. Fullwidth forms are separate Unicode characters (U+FF01–FF5E) that exist so Latin type can sit on the same square grid as Japanese characters. Typing ＡＥＳＴＨＥＴＩＣ means using different code points, not adjusting a slider.

So the effect is a side effect of a writing system doing its job, appropriated as a visual signature — and it has since become internet shorthand for the entire genre.

It is also distinct from the katakana and kanji that appear alongside it. Fullwidth Latin borrows Japanese typography's grid; actual Japanese type borrows the visual authority of the 1980s Japanese consumer market.