Ancient beers and other grain beers (rice, millet and so on) and non-grain beers (corn, cassava, fruit, so on) will blow your mind.
Hops are a flavoring for beer. Beer is the drink that results from the fermentation of wort (starchy water) without distillation. There are many many (millions) of ways to derive a wort.
Hops weren't even found in beer until the 9th century. Beer has existed longer before hops were introduced than since.
So we agree on the facts, but disagree on the precise meaning of words. Other than recreating ancient brews, it's moot anyway as all ale sold nowadays contains hops.
I occasionally brew in very small batches. I've brewed ales without hops, including one which was loosely based on an Ancient Egyptian recipe. Recipes here: http://web.onetel.com/~hibou/Ale%20Recipes.html
Nowadays, almost all ale has hops added and so is beer.