It's what cathedral's etymology is.

Words are defined by how they're used, not their etymology. Most people just use the word to mean any large church.

In fact, from dictionary.com: (2) (in nonepiscopal denominations) any of various important churches.

Also: Following the Protestant Reformation, the Christian church in several parts of Western Europe, such as Scotland, the Netherlands, certain Swiss Cantons and parts of Germany, adopted a Presbyterian polity that did away with bishops altogether. Where ancient cathedral buildings in these lands are still in use for congregational worship, they generally retain the title and dignity of "cathedral", maintaining and developing distinct cathedral functions, but void of hierarchical supremacy.

The term "cathedral" actually carries no implication as to the size or ornateness of the building. Nevertheless, most cathedrals are particularly impressive edifices. Thus, the term "cathedral" is often applied colloquially to any large and impressive church, regardless of whether it functions as a cathedral, such as the Crystal Cathedral in California or the Arctic Cathedral in Tromsø, Norway.