Snake Venom is beer not a spirit because spirits are distilled. Beer is technically not distilled.
As the definition you cited says, beer is the product of fermenting sugar derived from cereal grain which is dissolved in water. So water + grain + yeast = beer. The grain has to undergo a saccharification process where the carbohydrate chains (starches) in the grain are transformed into sugar (glucose, fructose, sucrose, maltose...) which is then converted into alcohol by yeast. Fermentable sugar is extracted from barley through malting and mashing. The yeast is generally added to the wort (unfermented sugary water) manually by the brewer or wild yeast can fall into the beer from the air.
Other processes may be involved with fermenting other grains. For example, in sake brewing, koji (a type of mold) is grown on rice (and soybeans) before fermentation in order to convert starches into fermentable sugars, as rice does not contain the enzymes needed to convert its starches into sugars (note: sake is generally not consider beer, but there are beers made with significant quantities of rice, up to 100% rice beer is possible).
Hops is not a necessary ingredient in beer, and beer was made for thousands of years before people started adding hops to it.
These strong beers like Snake Venom are generally brewed to this high ABV level through freeze "distillation." This isn't really distillation, because no heat is involved, so people still call them beers. But this is a concentration process similar to distillation. Alcohol has a lower freezing point than water, so when you freeze beer, you can remove the ice and you're left with a more concentrated beer. This is the process used in the German eisbock style. The brewers also start with a high ABV beer, using special ingredients (sugar sources other than malt, like table sugar) along with strains of yeast that can tolerate high levels of alcohol and still continue to live and ferment. This process can be somewhat difficult and expensive, so it gets attention. In my opinion it's a novelty, but I guess people like it, because they sell a lot of it.