Hey, I've beaten the game like 3-4 times now and don't want to spoil (though the IGN Guides videos of the walkthroughs are mine so I spoiled it all there if you want), but do think the divisiveness comes down to two things (one narrative thing and one gameplay thing -- and arguably the narrative thing also ties into the gameplay aspect):
ONE
-The game communicates frustrations about a time loop and the trial-and-error nature of it rather than the infinite possibilities of a time loop. It's inherently frustrating, and I think it plays in that direction because games as a medium are better at that than the infinite possibilities aspect. To put it another way, it's better at making you think you're Bill Murray in Groundhog Day and video games are not as good as making something like Groundhog Day enjoyable because you can't narratively construct something that takes out all the thousands of deaths like you do in a cohesive/linear movie. Now I think games can be pretty good at creating something closer to the cohesiveness of a time loop in Groundhog Day when the setting is big enough -- Outer Wilds comes to mind -- but this is so constrained in its setting that playing off the frustration is the angle they take (and I think rightfully so). Dying over and over again and feeling some frustration is not inherently fun though -- especially when there is some level of repetition involve and you're only doing point-and-click things throughout, and so I can see why the game will be divisive just starting there. However, I do think that game mechanic plays into the narrative and makes you as the player feel the frustration the character on screen -- or Bill Murray or whoever -- goes through. It's just it has to get you there through the act of playing the game rather than watching Bill Murray become disenchanted through the skill of quality film making.
There are multiple Edge of Tomorrow montage loops that sort of get at that frustration in the way this game does:
This isn't the montage I'm thinking of -- it's the one where Emily Blunt's character keeps dying and Tom Cruise's character is slowly just being drained of hope that's better, but the point stands.
On top of that, the dialogue system is flexible, but it's not so flexible that you don't run into some moments of dissonance where the character sort of has to repeat itself or act "shocked" all over again when you ask them a question you asked another way already in the same loop -- I hope that makes sense. This is more forgivable in a bigger setting, but you see how the branching dialogue trees still don't always mesh here in this very focused situation. This is the more "inarguable" reason for why the narrative doesn't always flow right. This is just an inherent flaw of games as a storytelling medium in this sort of story trying to be told. The possibility tree overwhelms even the skilled designer at a certain point -- at least in small ways.
Lastly, I did not find the puzzles overly challenging, and when I did get stuck I liked it because, again, it felt like how I would feel in that situation. I'm trying to slightly tweak the situation, and no the game doesn't always allow me to say everything I want or do everything I want when I think I should, but I never felt like it was a poor design. The closest I got to that is when I knew something and felt my character should as well, but I just hadn't re-clicked on something to make him have the same epiphany I already had. But for me, once I fail at a loop doing X thing, I don't keep trying it, and I suspect some people will be or have been more hard headed about it.
TWO
Beyond the gameplay, the narrative itself is dark. It gets darker as you go, and it's just, well, not fun to experience, especially after you hit a certain point and sort of see where it's all going. It probably should have a trigger warning, but maybe they didn't want to spoil where it was going. The "twist" is insane, and it's going to be the biggest point of contention. I'm still not sure if it was the right choice or if it needed to be the way that it is etc. but yeah they go for it. There are fake endings and a couple "true" endings that I've found so far, but the twist is basically the true turning point and there's no way to look at the characters the same way after it.
Beyond that, I think story vs. plot does play into things here. The "story" is not amazing to me, but the plot is very good in terms of putting the pieces together in interesting ways that I appreciate as a way to make me feel various things because 12 Minutes doesn't ever really say how you need to play it to get to the credits (until you actually get to them) -- again, like Groundhog Day in that way. You can play some loops as more dark comedy, others as horror, others as truly just F'd up, some as purely happy etc. it's flexible there in fitting into different boxes for those twelve minutes.
However, I don't think this game maybe has a great "story" message for what it's trying to say with all the plot, but I think the plot is engaging. Now, it's easy to say without story than the plot doesn't matter, but I don't think that's always true for video games like it generally tends to be with books or movies.