How is publicly shaming someone and aggressively lobbying for them to be fired not violent?
Violently going after someone's job would be punching their boss in the face until they agree to fire the person.
EDIT: Speaking from an American English perspective, anyway.
Definitionally, violence is physical. Redefining it to include non-physical acts is pure politics, and I for one will not let it pass without calling it out for the bullshit it is.
Wikipedia talks about nonphysical violence in the context of a "power relationship," where someone with a significant amount of power/control over the victim is the instigator. Things like emotionally abusive relationships. A bunch of people with no direct authority over you trying to get someone fired for inappropriate behavior doesn't fit that narrative.
If you told me people were violently going after someone's job, 100% my assumption is going to be "so they burned his garage down and threatened that his house is next unless he quits?" (or something along those lines). Calling phone calls and #FireBob tweets coming from people of no authority "violent" is an attempt at grabbing all the emotional baggage that comes with the word and attaching it somewhere that it doesn't belong.