That's why the deaths are almost entirely the very old and immunocompromised.
Could you provide a source?
Everything I've seen so far (eg, [0]) points to the virus itself damaging respiratory tissue, and normal body immune response aggravating that locally to some extent.
A cytokine storm [1] is, as I understand it, a massive systemic immune overreaction causing way too much inflammation, overwhelming the body all at once.
That Wikipedia entry suggests that SARS may have caused a cytokine storm, at least in some patients, but from it and everything I understand about the phenomenon, it's recognizable in epidemiology largely by the greatly increased incidence of deaths among young, healthy patients—which is not at all what we see in COVID-19.
[0] https://www.uticaod.com/zz/news/20200313/what-does-coronavir...