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My understanding of it is that They Changed It, Now It Sucks! is for whenever something gets changed - either in an adaptation, a sequel, a game update, etc. and some fans don't like it.
The problem with this example is that it doesn't explain how it's a fan reaction.
In defense of the specific example, we are talking about a sequel (or rather, prequel) here. In addition, there are aspects of Adam's personality/actions that were flat-out changed. For example, the entire axis their characterizations revolve around in Other M is that Samus left his command without his okay, which she's desperate to make up for and he seemingly resents her for. In the manga which originally portrayed the character, Adam was the one who suggested she strike out on her own and gave him her blessing.
That being said, I'm not defending the example from deletion or rewrite. Just playing Devil's Advocate.
The problem is that Adam's portrayal in Other M is completely different than in previously established canon. Fusion described him as a caring father figure to the protagonist, as well as a military genius. In Other M, the former trait is changed so he is cold and aloof towards Samus; whereas the latter is arguably absent, as his decision to split his platoon into weaker units culminates with The Mole picking them off one by one. I agree with the example, and I'm one of the only five people in the world who genuinely enjoyed the game.
The thing is, the trope is supposed to document fans' reactions to a change — that the fans saw a change, and said it sucked.
The trope is not supposed to be used to actually complain, "They changed this thing in a way that sucks."
It's TV Tropes recording the fan reaction; it isn't the fan reaction itself.
My impression was They Changed It, So It Sucks (per it's page) is supposed to be complaints that would seem overblown, nitpicky, arbitrary, or unfair to outside observers, and is knee-jerk against the mere act of changing as opposed to what is was changed to.
If it explained why Adam's characterization wouldn't have been as objectionable if not for changing his prior characterization, it would count.
Also, all that (intentionally) changed was retcons about being a parental substitute. He was ultimately portrayed (ie supposed to be seen) with the same positive portrayal as prior works. The hate and complaints are against the very, very poor job it did at portraying it, not the (clearly unintentional) change.
That's the issue I see with the trope, without clear rules to counteract the hate and negative emotions the trope covers it's interfering with the objective analysis of the work that is the purpose of the wiki.

YMMV.Metroid Other M
I think this is misuse as: 1. The work does attempt to portray him as "reasonable authority figure" who's becoming cold to Samus has an in-work explanation, it just does a very bad job at portraying it. 2. His characterization would likely have been just as unpopular even if it didn't replace his prior depiction.
The They Changed It, Now It Sucks! page sounds like it's only supposed to apply to changes in adaptations. But is seems like it's used for any complaints, the sort of thing that got restrictions placed on other tropes. Does it has such restrictions?