Considering the similarity of the questions and the opposite handling with regards to whether or not they are off-topic, there appears to be some discrepancy. What exactly constitutes being off-topic when it comes to these types of questions?
I'm sorry for not checking the site for a while. I reopened the question under scrutiny, and in my opinion, the others you cited should remain open as well.
As long as they are not open-ended (i.e. there is a definitive answer or study to be given, not opinion), such questions are suited for the Stack Exchange venue; therefore, the only objection that may remain is one regarding our site's scope. This is determined by the moderators. After the core topic is established (the game of chess), we have leeway in including/excluding related topics. So basically, it could change over time.
At this point, I call chess puzzles on-topic for chess.SE. But a few things could alter that consideration. The other moderators may disagree, or the chess.SE community may present a case for removing the topic, or some effect of that decision may prove to negatively impact the productivity of this site. But I don't see any of this happening, and chess puzzles have to do with chess, and I like chess puzzles.
There are several ways to enjoy chess. The most popular way is probably to play the game. Folk who do this often enjoy tactical puzzles which sample typical critical moments that might occur in a game.
However, just as both speed skating and figure skating are sports that involve moving around on ice, let's not forget chess problem composition. This has a venerable history, and titles (from GM downwards) are awarded for showing extreme technical mastery and artistic flair. Similarly, there are titles awarded for solving chess compositions, and while an OTB (Over The Board) player can achieve GM status in their early teens, it would be rare for a composer GM to achieve that before 40.
Compositions are deliberately not intended to be a "typical position from a game", and indeed it is very much frowned upon to add extra material to make the position more "realistic" - that's not the point. The word "puzzle" is deliberately avoided - there's nothing wrong with tactical puzzles, but that's not what compositions are about.
It may be that some kinds of composition may help in over the board play, but it's irrelevant and cringing to make that kind of argument. Does high-diving skill make someone better able to swim 100m freestyle? Almost certainly not, but high-diving is still a beautiful Olympic sport.
It's curious that even today, many competitive-minded chessplayers are snortingly ignorant that someone might want to engage with chess in a purely artistic way. In Magic the Gathering, at least a "Spike" (a.k.a. a competitive player) is generally aware that this is their designation, and that another designation exists: "Johnny" the player who wants to make cool decks that lead to interesting situations.
So there are Spikes in chess.stackexchange for whom the penny hasn't dropped, and still think "speed skating" is the only game in town. If they stumble across a composition post here in chess.stackexchange they may erroneously classify it as "off-topic".
I hope that (properly edited) my answer may be added to the terms of reference of this community, because it would be good to nail this misunderstanding once and for all.