That article (and the more general article on viruses) both pointedly avoid referring to viruses as organisms, "any living thing that functions as an individual".

<https://en.wikipedia.org/wiki/Organism>

Which specifically addresses edge cases including viruses, which "are not typically considered to be organisms, because they are incapable of autonomous reproduction, growth, metabolism, or homeostasis".

<https://en.wikipedia.org/wiki/Organism#Viruses>

Specifically, viruses have no innate metabolism, or energy-producing chemical reactions.

<https://en.wikipedia.org/wiki/Metabolism>

The terms "live" and "killed" have historical origins, but would better be read as "active" or "deactivated", and the immediately succeeding sentence clarifies this: "Live vaccines contain weakened forms of the virus, but these vaccines can be dangerous when given to people with weak immunity."

For more on the distinction see: <https://www.biologynotes.in/2024/03/difference-between-live-...>.

And yes, there are infectious agents which also happen to be organisms, such as bacteria, amoebas, funguses, etc. Tuberculosis (Mycobacterium tuberculosis), many stomach ulcers (Helicobacter pylori), botulism (Clostridium botulinum), and e. coli poisoning (Escherichia coli) are all infectious disease caused by bacteria. Giardiasis is a G-I infection of the Giardia amoeba. There are numerous fungal infections (many UTI infections, athlete's foot, jock itch, nail infections).

Further down the non-life infectious agent chain are prion diseases such as Transmissible spongiform encephalopathy ("mad cow" disease in cattle, "Creutzfeldt–Jakob disease", amongst others). These are literally misfolded proteins, which lack not only metabolism but any genetic material (DNA, RNA), but still propagate.

More on infectious agents, a/k/a pathogens: <https://en.wikipedia.org/wiki/Pathogen>.

A cell so minimal that it challenges definitions of life