My objection is to comparing it to lynching. Not on a technicality based on who is performing the act, but based on the existence of a fair trial. Versus a mob acting on mere accusation.
Of course trials at that time and place were anything but fair, but we don't generally refer to those state-run executions as lynchings (perhaps we should).
And how is any of that not torture? Seems like your definition of torture is just "doesn't result in death."
Anyway torture, simply defined, is an act causing extreme pain in someone. And not just for five seconds. Hanging-done-wrong can be torture. Many ways of killing someone are torture. But the fast methods are not. Tell me your definition if it can somehow apply to the use of a guillotine.