Also it's pretty clear that they don't care about eliminating the people - they want to eliminate the culture.
If I were an evil dictator with the means in the modern day and I wanted to really intimidate a population, I would abduct some of that population and just secretly kill them and burn their bodies. Nobody can then prove whether you actually killed them. You could say you re-educated them and then let them go, and their present whereabouts are no longer your business.
As to the larger question, most genocides stop short of literally just shooting everyone. That doesn't mean the goal still isn't eradication of a culture.
China does care about legitimacy internationally, and simply shooting millions of people into roadside ditches would be a step too far. But this process of concentration camps under the banner of combating terrorism is enough of a fig leaf, and enough of a slow progression, it doesn't generate the same sort of immediate opposition abroad. As we see here sadly.
But specifically in the case of Uighurs - you can eliminate a culture by erasing its identity, without killing the people. That seems to be what China is doing - they are not straight up killing them, just putting them in camps for "reeducation" so they behave and think like model Chinese citizens, with harsh punishments for following their original culture. That way, "Uighurs" as a group will be wiped out without necessarily killing them all.
Snyder’s Bloodlands is the definitive work on the subject. https://en.m.wikipedia.org/wiki/Bloodlands
The cost of a mass grave is that now the entire city knows you're killing people and you're coming for them. It leads to formation of resistance forces, kills your soldiers, stops the occupation from progressing.
Transportation is free because you took over the railways. Building concentration camps is free because it's done by literal slaves who have no choice anyway, and is done with local materials taken from existing housing. It's not like Nazis were paying market prices for any of this.
Like, I have no idea why were even arguing about this. Go and visit Auschwitz, it's all explained in the museum there. Read some books about occupations of Lvov or Warsaw - Nazis very quickly stopped executing people en-masse because it was more trouble than it was worth. You can say you disagree, but that's just arguing with facts.
"China isn't committing a genocide like the Nazis, because they could just shoot everyone. But, the Nazis didn't do it either, so the Nazis weren't committing genocide like those damn Nazis either"
Bizzare argument.
In this context it seems to mean that it's politically easier to "re-educate" the Uighar away than straight out kill the Uighars. If some die during the process China doesn't care but it can't be accused of genocide which would raise more concern globally.