It's more than that, slightly. A "serverless" application doesn't have a specific piece of hardware supporting it except in the context of a single operation. The hardware is all abstracted away and allocated from a pool on demand. I suppose it comes from "serverless architecture", where there are just other distributed services (not specific servers, virtual or otherwise) executing your code.

I agree it's not a term well suited to its popular use, but such is life. Commercial interests are constantly mucking up the language to suit their own ends. E.g. Discord is abusing the term "server" to mean a virtual meeting space. "Organic" w.r.t. food has a really contrived official criteria, unlike in chemistry. Regular people muck up the language in frustrating ways, too. See "literally".