I must not have made myself very clear either. Sorry, let me give it another shot. Yes, IMO your text does appear to assume that artisans are (upper) working-class. No, unlike you, I don't think of artisans as being (lower) middle-class. So it works fine for me.
>> Middle class, in England, people who have an
>> intermediate position between the aristocracy
>> and the artisan class.
In this sentence, from result #2 of the search you cite, "artisan class" is obviously used to mean "working class." But it's not a well-thought-out technical definition, just a loose paraphrase. (Perhaps even an attempt to avoid the term "working class.") Results #1 & #3, from Amer. Her. & WordNet above & below, gave more precise (and concise) definitions.
Word to the wise: That #2 section of dictionary.reference.com results was cited as "Webster's Revised Unabridged" with a supposed copyright date of something like 1996. But the entries looked both oddly short and rather dated (discursive) in style, so I checked, and they're actually from Webster's 1913, which is free (not to mention correctly referenced) online elsewhere. It's better than nothing, and sometimes a very useful source especially for odd or archaic words, but still not nearly as comprehensive as a modern unabridged dictionary.
>> classified as artisans
I assume you're aware that "class" as in group of similar items, categorization, is much broader and less technical than "class" as in social stratum. Artisans may be a class in the former sense, but IMO they're only a subset of a class (working class) in the latter.