Yes, the prose feels "artificially complex" because it's "literary nonfiction."
Your frustration is completely understandable. You can read sophisticated scientific publications and absorb information-dense Wikipedia articles easily, but this article feels awkward for you to read. The prose in the article could indeed be described as "artificially complex," but whether "artificially complex" is good or bad depends on your opinion of literary nonfiction.
Literary nonfiction is a type of prose that employs the literary techniques usually associated with fiction or poetry to report on persons, places, and events in the real world.
The Literary Article
Why does this article feel different than your average scientific publication? Why do I call it "literary"?
Exhibit A: The Phrase, "of the same name"
The first item on our list of literary aspects to examine is the phrase, "of the same name," which forced me (a native English speaker) to reread the first sentence twice.
SEPAHUA, a ramshackle town blah blah blah blah blah'blah blah blah, blah blah blah blah blah blah blah blah blah river of the same name blah blah blah blah.
This sentence states the name of the town at the beginning, then inserts the phrase "of the same name" towards the end, asking the reader to have kept track of the name from beginning to end. I posit that simply repeating the name "Sepahua" would more simply communicate the information, but I wouldn't call Charles Dickens "pretentious" for selecting a phrase like that for a novel. Maybe the author likes the sound of the phrase, or maybe the author wants to highlight the fact that the town and the river are connected -- more on that later.
Exhibit B: The Metaphor, "nestles in a pocket"
Next let's look at a more traditional literary device, the metaphor.
...a ramshackle town... nestles in a pocket... where [two rivers meet].
The metaphor "nestles in a pocket" evokes an image of a kitten snuggling into the folds of Grandma's apron. Compare that to the Wikipedia entry for an Amazonian city:
Manaus or Manaós before 1939 or (formerly) Barra do Rio Negro, is the capital city of the state of Amazonas in the North Region of Brazil. It is situated near the confluence of the Negro and Solimões rivers. With a population of more than 2 million, it is the most populous city of both the Brazilian state of Amazonas and the Amazon rainforest.
I'm not going to say that's a well written introduction, but if that's the type of writing a reader is used to, then "nestles in a pocket" will definitely feel like an awkward way to describe the geographic location of a town.
Before you proclaim that "confluence" is a randomly chosen Thesaurus entry for "junction," note that "confluence" specifically refers to the place where two rivers join. Again I'm not calling the prose here "good," rather the example serves to highlight why The Economist article feels different.
Also, consider why the author might want to give you the "warm, fuzzy feeling" from a phrase like "nestles in a pocket." The author is trying to transport the reader to the town.
Exhibit C: The Hyperbolic Quote: "maps are only in Lima"
Turn back to the Economist article to the quote in the last sentence of the first paragraph:
“Boundaries are on maps... maps are only in Lima”
While this quote doesn't convey a scientific fact about logging in the Amazon, the quote tries to give the reader some context with which to better understand why logging regulation has proven a stubborn problem. In the first paragraph, the reader learns about this remote town where local loggers scoff at big city regulators' attempts at drawing lines through the untameable Amazon jungle. Who knows if this quote accurately portrays the attitudes of professional Amazon loggers? For that reason the quote would be struck from a scientific publication. Still, the flowery imagery is meant to transport the reader to the Amazon jungle to get the needed perspective for the rest of the article.
Other Articles from The Economist
Scanning a few random Economist articles, I find that many, but not all, of the authors try similarly to give them a literary feel.
For contrast, consider this Economist Daily Chart entry, "Americans are richer than they were in the 1970s". The opening paragraph probably feels much more like the Wikipedia description.
AMERICA’S economy has grown massively during the past four decades, but not all of its workers have reaped the rewards. Perhaps the statistic most cited to demonstrate how unequal the gains have been is the median household income. Official statistics from the Census Bureau show that this number has remained flat for 40 years. However, a recent analysis by the Congressional Budget Office (CBO) found that it actually rose by 51% between 1979 and 2014. Why are the CBO's numbers so much cheerier?
Note that unlike the "Trade, timber and tribes" article, this article didn't dedicate an entire paragraph to a personal connection with someone affected by the information in the article. The information density of the sentences is roughly the same, but the diction and phrasing in the Daily Chart is more straightforward and plain. Even so, note that the word selection (e.g., "massively" and "cheerier") give the prose a bit more flavor than the Wikipedia article, but not so much that I'm looking for the nearest kitten to hug.
A Non-Literary Alternative Article
This article deeply disturbs the fellow who despises literary flourishes and emotional appeals. Not only the style, but much of the content of the article would be struck from an academic publication. If you cut through all the fluff in the article, you're left with two relevant facts that it's trying to communicate. Give it a sentence for context and a sentence of conclusion, and you're left with this:
In 2001, the government of Peru auctioned off logging rights in regions of the Amazon with 40-year permits to log 5% of the area each year. Recently, a report performed by Peru's forestry regulator found that only 22 of the 79 regions it investigated contained as much mahogany as the loggers claimed. Despite the underreported logging, a study by the Carnegie Institution, using satellite data from 2001 to 2005, concluded that the policy succeeded in limiting damage to the forest. This leaves reason to continue the policy, though questions remain as to how to increase enforcement to further reduce illegal logging.
(Side note: I wish I had read those 4 sentences instead of the article. For me it wasn't the style that bugged me, but the lack of meaningful content. Seriously, why on Earth is there a random paragraph telling me that there's still 15 uncontacted tribes in the Amazon? What does that have to do with deforestation?)
Back to your question: "Is the language of The Economist artificially complex?"
In answering your question, I've tried to show here that the answer is both "yes" and "that's not necessarily a bad thing." Furthermore I wanted to break down what I mean by "literary nonfiction," which I think is why this article feels different from Wikipedia and academic articles.
In terms of pure utility, both the style and the content of the article inefficiently conveys the relevant facts of the news story. However, for some people this style of writing is more enjoyable to read than something that more plainly states facts. Furthermore one could argue that literary techniques can more effectively (note: not the same as "efficiently") convey information, but that's subjective.
Your frustration with literary prose as a non-native speaker is understandable. Indeed, many if not most native speakers are frustrated right along with you. I suspect that "native English speakers who read The Economist" is not a representative sample of native English speakers in general.