Short answer: this is a mistranslation, and the original Italian contains the word ‘destra’ (meaning ‘right’) rather than ‘left’.
First, some background, since your comments indicate that there may be some uncertainty as to authorship and publication date of the article. I think the first paragraph of the English Wikipedia article sums it up nicely:
"The Doctrine of Fascism" (Italian: "La dottrina del fascismo") is an essay attributed to Benito Mussolini. In truth, the first part of the essay, entitled "Idee Fondamentali" (Italian for "Fundamental Ideas") was written by philosopher Giovanni Gentile, while only the second part ("Dottrina politica e sociale") is the work of Mussolini himself. It was first published in the Enciclopedia Italiana of 1932, as the first section of a lengthy entry on "Fascismo" (Italian for Fascism).
Thus, it should be noted that while the (purported) quotation was written by Mussolini in 1927, the earliest publication date is in 1932, and the only the second part of the article (from which your quotation is supposedly taken) is by Mussolini.
Wikisource has the entire text of this tract in the original Italian. Treccani also hosts an online text of the original 1932 encyclopedia article, in which (as the Wikipedia article mentions) Mussolini's essay is embedded. I cannot find your exact quotation within the text, but there is a very similar one:
Si può pensare che questo sia il secolo dell’autorità, un secolo di «destra», un secolo fascista...
This quotation occurs in Part 2, headed "Dottrina politica e sociale (di B. Mussolini, a cura di G. Gentile)" ("Political and social doctrine, by B. Mussolini, edited by G. Gentile"); it is thus clearly the work of Mussolini.
My translation of the Italian quotation:
One may think that this [i.e. the 20th century] is the century of authority, a century of ‘the right’, a fascist century...
Another translation, hosted at the the World Future Fund website, is transcribed from Mussolini's book Fascism: Doctrine and Institutions, (Rome: Ardita, 1935) an official Fascist government publication.
We are free to believe that this is the century of authority, a century tending to the "right", a Fascist century.
Fortunately Google Books has a snippet view of a scan of this publication, making it easy to check the accuracy of the transcription:
In your comments below this answer, you seem to be expressing disbelief that this passage actually occurs in the Google facsimile; please consult this imgur gallery for larger screenshots of the two relevant snippets, and here is a link to a Google search for the phrase "a Fascist century" in the book, showing that it is preceded by the word "right".
The quotation you posted is thus close to the original, but has substituted "left" for the original "right". The origin of this mistranslation actually appears to be another authorized translation by Jane Soames published by the Hogarth Press, London, in 1933 (facsimile here), which contains your quote exactly:
... and it may rather be expected that this will be a century of authority, a century of the Left, a century of Fascism.
I have been unable to discover how or why Soames managed to mistranslate "destra" as "left", but it is clearly incorrect to say that Mussolini himself stated this, or that it was present in the 1927 Italian original.
From your comments it seems that you lay great weight on the fact that this mistranslation occurs in an authorized English translation, so maybe it's worth mentioning what the term ‘authorized’ actually denotes: it simply means that the translation was done with the permission of the copyright holder. It doesn't confer any magical aura of perfection on the translation, and authorized translations, like any other translations, may be excellent, hopeless, or anywhere in between. For example, here's Arthur B. Evans summing up the quality of the authorized translations of Jules Verne:
In a rush to bring his most popular (and profitable) stories to market, British and American translators repeatedly watered them down and abridged them by chopping out most of the science and the longer descriptive passages… they committed thousands of basic translating errors, mistakes that an average high-school student of French would have managed correctly; they censored Verne’s texts by either removing or diluting references that might be construed as anti-British or anti-American; and, in several instances, they totally rewrote Verne’s narratives to suit their own tastes (changing the names of the characters, adding new scenes, deleting others, relabeling the chapters, and so on).
I hope that makes it clear that ‘authorization’ counts for nothing in terms of accuracy. Indeed, we have two authorized translations available (Soames' from 1933, and the version published in Rome in 1935) which clearly contradict each other in this sentence, so they can't both be right!
In the case of your quotation, we fortunately have the original Italian available, so there's no need to rely on the accuracy of any existing translation; anyone with access to an Italian-English dictionary can easily check what ‘destra’ means for themselves.