After I posted my question here, Russia's state news agency, TASS, published statements of Putin's spokesman, Peskov, about the matter in question:
Песков отметил, что Путин, заинтересовавшись этой темой, "работал с Росархивом, с разными историками, большая часть работы была проделана самим президентом". "Не то чтобы он сам сидел в архивах, но он живо знакомился со всеми архивными документами, которые ему передавали", - добавил представитель Кремля.
Peskov mentioned that having become interested in the topic, Putin "worked with the Federal Archival Agency and various historians, and a large part of the work was done by the president himself." "He didn't really spend time in the archives, but he vividly acquainted himself with all archival documents that were brought to him," added the representative of the Kremlin.
So Putin's spokesman confirms that the article was a result of joint work that involved "various historians."
Interestingly, the news publication goes on to quote Peskov's explanation of why the English version of the article, published in The National Interest, and the Russian version, published on the Kremlin website, provide different numbers of Russian casualties in the Battle of Rzhev:
Отвечая на вопрос о причинах разных данных о потерях СССР в Ржевской битве в годы Великой Отечественной войны в англо- и русскоязычной версиях статьи главы государства, Песков пояснил, что в журнал National Interest англоязычная версия статьи была отправлена заранее, "а работа в архивах по уточнению данных о погибших продолжалась фактически до последнего часа, когда уже в издательство отравлялся русский, аутентичный текст".
Answering a question about the reasons why the English and Russian versions of the article by the head of the state provide different numbers of the USSR's casualties in the Battle of Rzhev, fought in the Great Patriotic War, Peskov explained that the English version had been sent to The National Interest earlier (than the Russian version had been sent for publication elsewhere), "whilst the work in the archives to get more accurate data regarding casualties had continued practically till the last hour before the Russian, authentic text had been sent to a publishing house."
So Peskov says that the original text was written in Russian. And if it's true, it's hard to imagine that the president himself spent time and effort translating the Russian text into English, especially given that he isn't a professional translator.
A comment by User under my question provides a link to a video in which Putin answers in English a question by a journalist of Sky News. Here is the relevant moment in the video, and here is my transcript:
Journalist: Mr. Putin, how worried are you that the protests will affect your election victory? Are you concerned?
Putin: No, I am not concerned. I think about people, ordinary people of Russia. Of course, I see the protests, groups, and I think about it, what I can to(sic!) do with(sic!) all our citizens.
Interestingly, the Russian subtitles translate the last sentence into Russian as, "Конечно, я вижу группы протестующих и думаю о том, что я могу сделать для всех наших граждан," which means, "Of course, I see groups of protesters and think what I can do for all our citizens."
Such a level of English language proficiency is clearly not enough to write the English text of the article in question, although it should be noted that the video was shot in 2012. Putin may have improved his English language skills since then, although he was already 60 years old at that time.
Finally, I discovered that it's not really uncommon for newspapers and magazines to publish articles by politicians who don't speak the language of the article, and without acknowledging the translator. For instance, Pravda, a Russian newspaper, published an article authored by Sen. McCain and written in Russian and for Russians. The article is titled "Россияне заслуживают лучшего, чем Путин" ("Russians deserve better than Putin").
So in view of all the evidence and the answers to my question I find it extremely unlikely that Putin himself worded the English text of the article, although he may have contributed to the original Russian text, most likely by giving some general guidance, making corrections to better reflect his foreign policy agenda, and approving the final version.