It's the previous DNA analysis that was based on just mitochondrial DNA - This one isn't. It's based on what is allegedly a new improvement in DNA testing, but it involves testing conventional nuclear DNA. Also, given the rest of Kosminski's history, if he was, say, merely a pimp who was wounded at the same time as the death of one of his prostitutes, his subsequent behavior was rather unlikely, to say the least. He was suspected of being Jack while he still lived. I don't know about you, but if the police were looking into the possibility I was Jack the Ripper, and the real Jack had tried to kill me, then proving my own innocence by giving them information that might lead to the real killer looks a lot more rational than shutting up about it. It's pretty much killing two birds with one stone at that point. (As opposed to Jack's method of killing birds, I guess). There are people pointing to K's mental illness history, and how he might not be particulalry rational, but there's a big difference between saying someone is mentally ill, and saying, they were mentally ill, and it was definitely in a way that would make them not do what most people would do here, but definiitely also not in a way that would make them commit murder either.
People taking the other side have to either beleive this new evidence isn't a real improvement in genetic testing and that claim is essentially false (which is fine by me if they do - time will settle whether it is or isn't), or they have to make some pretty bizarre and often self contradictory claims about the few other items of evidence we have, such as claiming Kosminski was a real bad apple who the police wanted enough for very serious crimes (just what, they never wrote down), that he couldn't have whitewashed his own reputation even by giving them Jack, or that Kosminski had some major underworld contacts who would have paniced if he had gone to the police (but these contacts couldn't take care of the Ripper if Kosminski went to them instead). ,
Other such evidence that has to be tweaked is there are some good sketches of the crime scenes, and for this one Jack had to, for example, fight Kosminski only in places where it was too dark to see his face, then kill the prostitute and move her body indoors past some well lighted areas without K hanging around to see who the real Jack was, and do it all quickly enough that the real Jack could get out of there before K could have returned with the police. (Or somehow, the real Jack had to know K was not the type to return with police, or something else both odd and very much not in evidence.).
There's also the claim which has been around for decades, that the word Jewes in the grafitti scrawled at one crime scene has to refer to some Masonic ritual and not be a misspellling of Jews, and other such things which have always been oddish speculations, but had better be taken as basic assumptions to make it less likely that K did it - people who seriously want to claim there's no other evidence than this 'questionable' DNA test to link Kosminski will just about have to buy into one or another of these oddish assumptions like the "It had to be a Mason" bit, as well. People willing to go down such roads usually end up "proving' that jack was Queen Victoria, or the Loch Ness Monster, or other such candidates.