Just like yelling "fire" in a crowded theater (where there is no fire), sending someone a gif in the hopes that it causes a seizure is not protected speech. It's assult.
I agree that the first amendment doesn't apply in this case, but the "fire in a crowded theater" analogy is only used by people who aren't aware of its origin. The phrase was coined by Justice Oliver Wendell Holmes in WWI, in a SCOTUS decision to imprison socialists for leafleting against the draft.[1]
Slippery slope. If I tell someone on the internet to kill themselves and it turns out they're actually suicidally depressed, should I be charged with a crime?
What if I post something that's just really offensive? I feel like we've entered a time where people would gladly see the First Amendment trodden over if it means seeing "justice" doled out to nasty people.
Eichenwald didn't "turn out" to have epilepsy – he had written about it before. This was someone intentionally attempting to harm someone by triggering a seizure.
And your hypothetical situation isn't hypothetical – people who cyberbully others into committing suicide are certainly charged for their crimes.
This isn't even close to a gray area! The analogy would be finding out that your target is in a given theater, where you then yell "fire!". This was targeted and pre-meditated; the result and the intent were one and the same.
1. https://en.wikipedia.org/wiki/Schenck_v._United_States