That's not hyperbole, it's just the wording directly out of the law they're charging him under:
https://www.law.cornell.edu/uscode/text/18/2261A
And in full context it says:
… engages in conduct that—
…
(2) with the intent to kill, injure, harass, intimidate, or place under surveillance with intent to kill, injure, harass, or intimidate another person, uses the mail, any interactive computer service or electronic communication service or electronic communication system of interstate commerce, or any other facility of interstate or foreign commerce to engage in a course of conduct that—
__(A) places that person in reasonable fear of the death of or serious bodily injury to a person described in clause (i), (ii), or (iii) of paragraph (1)(A); or
__(B) causes, attempts to cause, or would be reasonably expected to cause substantial emotional distress to a person described in clause (i), (ii), or (iii) of paragraph (1)(A),
So they're not trying to prove "intent to kill". They only need to prove "intent to intimidate anther person" using an "electronic communication system of interstate commerce" that either for (A) "places that person in reasonable fear of … serious bodily injury", or for (B) "would be reasonably expected to cause substantial emotional distress".
Seems to me they've laid out all the evidence needed to show that - the only thing a court needs to decide is if that evidence is all true and admissible.
I wouldn't want to be the defendant here.