Reading the material, I saw references to "injury" in London. Had she amended / updated her complaint for some alleged 'injury' during the Olympics?
Her original complaint alleged violations of New York State and City human rights laws. After the Olympics she amended it to add a claim of assault. This is the "injury" the court speaks of in assessing where (for jurisdictional purposes) the alleged wrongful act took place.
It is not a physical injury in this sense. The court means simply the harm complained of.
Bear in mind that, for legal purposes, an assault is not what the average person thinks it is. It's basically only a
threat to do imminent violence, such as waving a club at someone. If accompanied by actual touching, such as hitting, it becomes an "assault and battery."
Specifically, Hardwick alleged that Geno "screamed" at her and pointed his finger at her in a threatening manner.
According to the allegation, he was demanding she move from where she was sitting in the stands at a practice. This was part of an ongoing dispute they had over where she sat (too close in his opinion) and how involved she got (cheering, etc.).
Her characterizations of "screaming" and the ominous pointing (I'm sure she was terrified) are of course rather subjective.
As I see it, he may not have wanted cheers for particular plays in practice (maybe they were good plays in her eyes, but not in his), or for any plays, found them a distraction and interference and didn't want her participation.
And that's aside from whether she was doing her job as a security officer. One can imagine that while playing the involved fan she'd have noticed a terrorist only if he came up and tapped her on the shoulder.