People died, yes...from heart attacks. The only death they know of that was a direct result of violence is Ashli Babbitt who was shot trying to enter. 5 deaths, 3 of which were heart related, Babbitt being the 4th, and the last being the unfortunate death of Officer Sicknick. While he was struck in the head with a fire extinguisher, just a few weeks ago Newsweek reported it was still unclear what the cause of death was as other health factors may have contributed to his death.
Trump called for the protesters to disperse multiple times during the fracas, and any calls he made to stop the transition of power prior were vague at best. It's one of the reasons they couldn't make the impeachment stick. An insurrection is defined as "an organized attempt by a group of people to defeat their government and take control of their country, usually by violence." There was nothing organized about that group of people, they didn't have a plan and they dispersed as soon as the NG told them to leave. Violent? There were a handful that were violent, but it was a mostly peaceful protest (See what I did there?). Again, for all the pearl clutching over 5 deaths only one was confirmed as a direct result of violence, that being Babbitt. That doesn't mean the deaths weren't unfortunate and preventable, but citing the deaths is kind of silly when only Sicknick's death can be attributed to possible violence by the protesters. He was still able to return to the station afterwards as oppose to going directly to a medical facility, which lends itself to the fact his cause of death is still unconfirmed.
So, no, insurrection isn't the exact word because it doesn't fit the definition.
