It would be accurate to describe this as a "tribute" as most of the speed manipulated remixes are faithful to the original version (using literally an original track).
This is a recent phenomenon that has been around since the dawn of the internet, and it's quite a polarizer if it isn't used well. A nightcore remix is a bit like a simplified happy hardcore; it seeks to pitch up and speed up the song to give it a danceable impression whereas its inverse sibling, the slowed and reverb and/or vaporwave slows and pitches down the song to give it a usually melancholic and nostalgic impression.
To some of them, they may seem uninspiring, boring, perhaps campy, but it is a testament of an idea when you take an arrangement and manipulate it, the overall 'vibe' or impression seems to change drastically (e.g. Vanilla Fudge covering The Supremes, Lee Scratch Perry's dub remixing).
A recurring trope of nightcore when published as a video is a photo of an anime character that might be unrelated to or related to the content of the song.
Now... I think this will shut the critics' mouth up when they hear ABBA Voyage: Nightcore Edition.
Liebezeit, are these "remixes" (??) meant to be taken seriously? It reminds me of times when as kids we used to play the 33rpm records on 45rpm and vice versa and laughed at the funny voices it created. Indeed, the above version of Don't Shut Me Down sounds like a Mickey Mouse cover
Michal , As seriously as Spike Jones and his City Slickers. They should be treated as a novelty - but I've no problem with someone who would like to use it to the fullest potential. Some official slowed and reverb remixes have made their way to the contemporary artists.
I'd say that these remixes are much like a trend meant to impress the audience, but that sort of got oversaturated (like most trends) to the point of annoyance. When used in the current context, with the awareness that nightcore or vaporware are passé, it might tend to bring out its ironic quality.
The original poster (for the Don't Shut Me Down nightcore) seems to be aware that he's not too serious about it; their channel description speaks for itself.
I can also remember being fun with the turntable (it ran 33 and 45 too) and getting the records to play at a different speed. I'll admit, some records do sound better at extreme speeds of the opposites, and found some of Frida's tracks to be compelling at 16rpm.
But for each humourous act, I see an advantage for a musician... I had a shellac disc of an R&B artist that was running at 78, and I had to digitise it until I could pull up Audacity to bring up the speed to what it should be. It was fun to hear the music stretched out, and entertaining too - it also reminds me of the anecdote of what some musicians were doing before the internet, where they had to rely on a record (never mind sheet music) to know their cue and notes.