<tl;dr> It's something else, namely a contributor to Wikipedia writing himself into a corner and then trying to use a punctuation mark to free himself. The basic confusion is the writer's.
The participial clause is a nominative absolute. Nominative for any subject of the participle that might be present, and absolute meaning independent of the grammar of the main clause. Let's start with a simple example:
[1a] Having previously attached his chain, the tall man towed the car away.
The absolute is loosely associated with the grammar of the main clause, serving an an adjunct to the subject man, meaning
[2a] The tall man who previously attached his chain towed the car away.
or serving as an adjunct of time to the verb, meaning
[2b] The tall man towed the car away after he had previously attached his chain.
or you may consider that the absolute is serving in both capacities.
The absolute in 1a doesn't have its own subject, and in the pre-position (at the head of the sentence), there's a strong presumption that the missing subject is the same as the subject of the main clause: the man who attached the chain and the man who towed the car away are the same person.
In the post-position (at the end of the sentence), however, we may need to rely on grammatical, semantic, or stylistic considerations to find the right subject. For the following sentence:
[1b] The tall man towed the car away, having previously attached his chain.
The car is not an option. The personal possessive pronoun doesn't apply to inanimate objects, cars don't attach chains to themselves, and the word previously directs us to earlier in the sentence, before towed.
Notice that these clues won't help in the pre-positions that we call dangling:
[1c] Having previously attached his chain, the car was towed away by the tall man.
Here we're left with the slight but ludicrous suggestion that the car attached the tall man's chain to itself.
The sentence cited by the OP would be clearer with the participial clause in pre-position:
[3a] Having a more soothing, somewhat light-hearted feel, the poem is well-known for its departure from Owen's famous style of including disturbing and graphic images in his work.
There's no doubt in this case, that it's the poem with a light-hearted fees. There's actually nothing that bars post-positioning, but the intended subject is farther away and the attachment isn't as strong. Consider the following:
[3b] The poem is well-known for its departure from Owen's famous style, instead having a more soothing, somewhat light-hearted feel.
In this truncated version, there's a slight ambiguity. What's having the light-hearted feel? "The poem" is a candidate, but so is the poem's "departure" (from Owen's usual style). The latter is closer, but either choice is apt. The problem arises with the long version in the original:
[3c] The poem is well-known for its departure from Owen's famous style of including disturbing and graphic images in his work, ___ instead having a more soothing, somewhat light-hearted feel to it in comparison.
Now the proximate referent is Owen's "disturbing and graphic images," and they are definitely not soothing and light-hearted*. So I believe the writer of the entry tried to fix things by repeating the subject, the poem, in the slot I left empty. The writer also preceded the inserted subject with a semicolon, which is a punctuation mark that can signal that a clause with its own subject is to follow. Unfortunately, that following clause should be an independent clause with a finite verb. Something like:
[3d] The poem is well-known for its departure from Owen's famous style of including disturbing and graphic images in his work; instead the poem has a more soothing, somewhat light-hearted feel to it in comparison.
(In the examples 1a-1c and 3a-3c, the nominative part is missing: the participial clause has no stated subject. Subjects are permitted and common:
[4a] His chain having been attached, the tall man towed the car away.
The association with the subject of the main clause is slightly weaker. We don't know who attached the chain. It could have been the tall man's short assistant.)
* Understatement department. Here's the first line of Owen's poem "Anthem for Doomed Youth": What passing-bells for these who die as cattle?