Here's a longer version of the same article, that has a bit more clarity:
Though Giuliani is not disputing that the statements were false, he does not concede that they caused any damage to Freeman or Moss. That distinction is important because plaintiffs in a defamation case must prove not only that a statement made about them was false but that it also resulted in actual damage.
Moss told the U.S. House committee investigating the Capitol riot that her life was shattered by the false accusations. She said she received hateful and racist messages, some “wishing death upon me. Telling me that I’ll be in jail with my mother. And saying things like, ‘Be glad it’s 2020 and not 1920.’”
Freeman said in her testimony: “There is nowhere I feel safe.”
Giuliani’s statement was attached to a filing arguing that he did not fail to produce evidence in the case and should not be sanctioned as Freeman and Moss had requested.
“While Giuliani does not admit to Plaintiffs’ allegations, he — for purposes of this litigation only — does not contest the factual allegations,” the filing said.
Giuliani political adviser Ted Goodman said in an email Wednesday that the filing was made “in order to move on to the portion of the case that will permit a motion to dismiss.”
Note the bolded statements.
This seems very legalistic, as if in this context, Giuliani is "not disputing the statements are false" in a legalistic way "for purposes of litigation only", "in order to move on to the portion of the case that will permit a motion to dismiss."
As a layman and not a lawyer, it sounds to me like he cannot definitively prove these two voting center women were rigging votes as Giuliani accused. (Even though there are tens of millions of us who all saw the camera footage, and it sure as hell looks like vote tampering. But maybe since Giuliani cannot PROVE that the video evidence clearly shows vote tampering, Giuliani is saying it was wrong to allege it was tampering without more evidence, which legally equates to Giuliani making a false statement, that he is withdrawing without severe penalty by the court THAT PORTION of what he alleged, not that he lied, but that he without enough proof made a false statement, and stated that to the court so the dispute about that portion could be resolved "for purposes of litigation only", and "in order to move on to the portion of the case that will permit a motion to dismiss" so Giuliani could resolve that portion that was preoccuppying the court, and move on with the part of the case he had evidence to prove.
And that the liberal media and Democrat leadership spin as "Giuliani LIED".
Despite the judge manufacturing a charge of false statements by Giuliani, for asserting in court the opinion argument that he (and Trump) firmly believe the election was rigged (as do I and as do at least 74.3 million others, as well as millions of other independents (in polls 51%) and Democrats (in polls 30%).
A plea made to circumnavigate what the (Democrat) judge refused to accept as Giuliani and Trump's first amendment opinion, the judge made Giuliani plead to making a false statement, to get past it and continue with the major thrust of Giuliani's case at trial.
I'm not a lawyer, but clearly the language shows Giuliani did this for convoluted legalistic reasons demanded by the judge, not because Giuliani is guilty of anything.
