I think it is concluding a train of thought which begins a little prior.

1: is the material situation on the scale that genocide can be considered? YES

There is a brief overview of the extreme violence. Including para 49 which quotes five paragraphs from UNRWA, “The Gaza Strip: 100 days of death, destruction and displacement” followed by the WHO, other orgs etc. Including:

“Gaza has become a place of death and despair."

" 93% of the population in Gaza is facing crisis levels of hunger.. Starvation, destitution and death are evident"

"the largest displacement of the Palestinian people since 1948"

It is concise but compelling. Anyone should read these pages if you haven't. Zero ambiguity. In numbers and suffering, the scale is sufficient.

2: Is there a genocidal vibe? YES

Then in 51, on to the immaterial component of genocide. During the hearing, Israel casually dismissed assertions that the evidence "genocidal intent" SA provided was just some random celebrities with no authority and they didn't speak for the nation. ICJ provides "statements made by senior Israeli officials" (Gallant, Herzog and Katz). They are dehumanizing, describing collective punishment, and explaining how they plan to enact the punishment via the military:

"We are fighting human animals"

"It is an entire nation out there that is responsible. It is not true this rhetoric about civilians not aware, not involved. ... we will fight until we’ll break their backbone"

"They will not receive a drop of water or a single battery until they leave the world."

Then UN statements from Oct-Nov 2023 indicating that the resemblance to genocide connected to the government has been publicized by credible orgs for a while now and surely Israel is aware:

"discernibly genocidal and dehumanising rhetoric coming from senior Israeli government officials"

"racist hate speech and dehumanization directed at Palestinians"

3: why these orders in this situation

54 concludes by saying the situation is "plausible". I interpret as "fucking obvious". In 56 they summarize SA's arguments about why the punishment fits the crime. 2 reasons:

to ensure compliance by Israel with its obligations under the Genocide Convention

protecting the integrity of the proceedings before the Court and South Africa’s right to have its claim fairly adjudicated

Which is saying the genocide is going on now and we need to stop it now. And a legal argument about prejudice means that if you don't take this action now, it will be impossible to do it later. So it would be "pre judged" against the interest of one party (Palestinians). Not articulated but clear is the reason: if Israel succeeds in it's stated objective to "eliminate everything" (Gallant) then there will be no witnesses, no evidence, and no population left to obtain the judgement. There is urgency.

4: why israel is full of shit

Then to 57 which you quoted above. Most key is the Israel argument that

the measures requested go beyond what is necessary to protect rights on an interim basis and therefore have no link with the rights sought to be protected

they think it would be unfair for them to be hobbled as is requested. They say they are engaged in a legitimate war just like many other nations have done and they should not be singled out. Even though there are deaths and suffering, it is an unavoidable part of obtaining military objectives. It is not motivated by deep hatred of all Palestinians. And this hatred does not fuel them to engage in activities whose only goal is to eradicate them.

As per the logic described above, the ICJ disagrees with Israel:

Therefore, a link exists between the rights claimed by South Africa that the Court has found to be plausible, and at least some of the provisional measures requested.

The court is drawing a strong connection between the heinous shit the politicians are saying and the outcome of tremendous suffering at the hands of the military. It is quite decisive considering how short the hearings were.