> To "run cloud?" Does this mean treating your own servers like "serverless?" Does it mean running Kubernetes? Is this primarily for people who want to self-host LLMs?

Machine/system/service deployment via API.

See §Essential Characteristics

> On-demand self-service; Broad network access; Resource pooling; Rapid elasticity; Measured service

* https://en.wikipedia.org/wiki/Cloud_computing

None are generally applicable to standalone pizza boxes as managed individual (as opposed to being herded by (e.g.) OpenStack).