Saint has the difference between assault and battery basically correct, though it's missing the word "imminent". Your victim must believe that he is in imminent danger. Even if I see you in a Super Market and say that I am going to go get a gun from my trunk and return in less then a minute to put a bullet in your ass, I haven't committed assault. Unless I appear to have the intent and capability to carry out my threat at the exact moment that I make the threat, it's not assault. Thus you could never be guilty of assault based on a mailed letter unless, I suppose, the letter said, "I know you open your mail in your office. Well . . . guess who's hiding behind your desk with a length of piano wire, Dead Man?". Frankly, it's questionable whether even that would be assault . . .
In this case, you'd also have a problem because none of the intended victims knew about the letter, as far as I can tell. The person being assaulted must be put in an apprehension of an imminent harmful or offensive touching. If I walk up behind you and point a loaded pistol at the back of your head, I haven't assaulted you because, while you were definitely in danger of an imminent harmful or offensive touching, you never had an apprehension of it. That is how I think I would characterize all the innocent people at the Superbowl who might have been injured by this guy.