Well, it's mostly from my guess that any functioning industrial, technological society comparable to our own (or at least, that of boom years of the 20th century) is likely not going to be
overly exotic in the nitty-gritty,
compared to our own—if it could exist, it likely would have out-competed and supplanted it's mundane counterpart, a la the Competitive Exclusion Principle. And if a comparatively exotic system could coexist
without supplanting mundane industrial society, then, well, it's not really a true counterpart. Like how the existence Hippie Communes really wouldn't be invalidated by the continuing existence of Industrial Civilization...but they're really anything more than a niche alternative, not a true challenger.
But! That's all sleep deprived, pie-in-the-sky rambling...the real meat of what you were asking? In regards to the aesthetics of an Automat in a Sinicized/Islamicized alternate world?
Utilitarianism. In that, things that have demonstrated utility, and are cost-effective (read: "cheap"), have staying power. And if "form follows function," a hammer is going to look like a hammer, and a metal box is probably going to look like a metal box, no matter what parachronic civilization builds it, if they're still human. And a general lack of ornamentation or unique cultural flavor might, in the end...take a back seat to selling mass produced bento boxes to urban office workers on their lunch break, with a relative minimum of overhead cost.
In a universe where there's a giant statue of Guan Yu standing magnificently in place of the Sutro Tower, there's very likely a souvenir stand or five within walking distance, and certainly a wood-frame bar down by the harbor that doesn't look or function appreciably different from one on the same spot, thirty universes in either direction.
And the angels, all pallid and wan,
Uprising, unveiling, affirm
That the play is the tragedy, "Man,"
And its hero "Boring, But Practical."
Oh! The year for the pic is—
according to a deep, detailed research project consisting of skimming through wikipedia and Google Translate—the current "Huangdi Year," the years since the start of the reign of the semi-mythical Yellow Emperor, minus 77 years. Or, 1945 AD.