This is a combination of bad layout and ambiguous punctuation.
The phrase is meant to be parsed as "(sour, by implication) cream and onion in the American style". Because the adjectival phrase "American style" is broken across two lines, miscapitalized, and does not have a hyphen in the adjectival phrase, the implication by layout is that "style", to use a programming term, binds more tightly than the full phrase, leading to the false conclusion that "style cream" is something that exists. This should have been laid out as
American-style
Cream and Onion
Flavour
to ensure that the phrase wasn't misinterpreted. Note the hyphen and lower-case "s" in style, which says "this is a single adjectival phrase, to be parsed as a unit".
American Style
Cream and Onion
Flavour
would have communicated the intended meaning, despite being ambiguously punctuated, because the layout implies the association of "American" and "Style" instead of "Style" and "Cream".
I'd guess this was the original layout, and someone tweaked the font size up, causing "Style" to move to the next line; the tweaker, not knowing the English rules for adjectival phrases, decided to move "style" to the second line because it was "looked nicer" (one word on top, one on the bottom). The little "new" flag was probably also an unconscious impetus to break the line after "American", as it crowds the first line a little.
To be completely accurate, this should have been
American-Style
Sour Cream and Onion
Flavour
There, that's thoroughly over-analyzed.