Assuming Conde Naste (publisher of The New Yorker) were to protest, this case would be one for the books. The article states that there is no foreign language edition of The New Yorker (which is not to say that the English version doesn’t find its way to Russia).
Assume for the sake of argument that CN has Russian registrations for the cyrillic translation AND transliteration of NEW YORKER, this mark isn’t either (and would such registrations be valid if never used?).
Typeface similarities between roman and cyrillic? Compare the O’s and the E’s.
Look and feel of the magazine as a copyright concept?
A series of magazine covers as a famous trademark? (it’s difficult to get protection for non-traditional trademarks under Article 6bis, the argument being that the treaty can’t protect the types of trademarks that weren’t recognized when the treaty was signed).
If only the Russian magazine would publish a drawing of Eustace Tilley looking at a butterfly through a monocle, then this would be an easy case. New Yorker covers here.