Wrongly isn't wrong here, but someone seeing the title of the video without understanding its context might be rightly confused for two reasons: wrongly isn't an expected collocation and without the context wrongly and wrong are ambiguous.
Wrongly was not the collocation you were expecting.
Wrongly may be unexpected here because of the common use of the flat adverb form wrong. A flat adverb describes an adverb that lacks the -ly suffix that marks most adverbs derived from adjectives. The flat adverb looks indistinguishable from an adjective, which is why prescriptive grammarians in the 18th century discouraged its use. (Compare: "I ran quick" and "I ran quickly." The first is used commonly in informal speech but discouraged by many editors and grammarians in formal contexts.)
Despite such discouragement of flat adverbs in general, wrong as a flat adverb is more common than the adverb wrongly: the Corpus of Contemporary American English has instances of the adverb wrong 10125 times (out of 93754 results for wrong), and wrongly appears 1645 times.
These results suggest that wrongly would be a less expected collocation for English users. A Google search for "voted wrong" and "voted wrongly" confirms that "voted wrong" has around 25,000 results and "voted wrongly" has around 10,000. COCA has three results for "voted wrong," all in spoken situations on CNN or CBS news/current event shows. "Voted wrongly" does not appear, indicating that it might be less common in journalistic or media use. As a result, readers and listeners might expect wrong rather than wrongly and perhaps they'd even expect another adverb before wrongly. These expectations can affect initial judgments of appropriate usage.
Both wrongly and wrong have ambiguous meanings here
A given action or event can be done wrong(ly) in several ways. Did someone vote wrong(ly)
procedurally, that is, they mishandled the ballot in some way?
politically, that is, they voted for a candidate or issue that the speaker considers wrong?
criminally, that is, they voted when they were not eligible to vote
ethically, that is, they approach the act of voting in a way the speaker considers invalid or immoral
There are more possibilities. Both wrong and wrongly have issues with ambiguity, such that having this as the title of the video is less precise than using a more specific adverb or qualifying the adverb with more explanation. So why did the video preparer (Einblick) go with wrong or wrongly?
The context determines how wrong and wrongly are understood
Consider the larger context. One reason wrong/wrongly is used is because the term appears several times as an adjective and adverb to describe voting habits fairly early in the video. I type out the relevant snippets that, indeed, start at 1:40 in the above video:
(Murray) voting the wrong way, voting for the wrong parties ...
(Einblick) this is a concept of (rote?) voting wrong
(Einblick) people have developed this idea that people vote wrongly when they haven't been informed yet in a proper way
Einblick is caught up in the usage and repeats it, while Murray moves on to explicate why the claim that people vote wrong(ly) is a simplification of opponents' political arguments and issues. "Wrong" becomes one of the key charges in this discussion, but it takes listening quite carefully to both Murray and Einblick to figure out exactly how the wrongly in the video title should be taken and whether Einblick's paraphrase is correct.
It's a matter of opinion whether such a video title is enticing (people will watch because they want to know why Murray says people vote wrongly), misleading (it's unclear exactly what "wrongly" means), or both, and that uncertainty that may be at the root of your discomfort with its usage here.
