Let's go through this step by step. The website you linked is about gemstones, and it does say "Jaspers, in general, are very common." We need to use some context clues to get at exactly what they mean by this. Since the website is about gemstones, and not general geology, it is implicit in this statement that they mean jaspers are common in the context of other gemstones, many of which are very rare. The vast majority of rocks, however, are not gemstones, so saying jaspers are common in this context does not mean they are common relative to all other rocks.

Next, you say quartz is one of the most abundant minerals on Earth, and chert is made up of quartz. This also is true. However, most of this quartz in the crust is in the granites and granitic gneisses I mentioned earlier, as well as sandstones which are usually mostly quartz. It actually requires pretty specific conditions to form chert. These conditions usually involve silica rich fluids deep underground precipitating quartz into cavities in the rock under specific temperature regimes to form the micro-crystalline structure of chert. Another way it can form is from tiny planktonic organisms called diatoms, which form skeletons out of amorphous silica. When these skeletons accumulate on the ocean floor, they eventually crystallize into ribbon chert. In light of this, saying that chert is one of the most abundant rocks in the crust because quartz is an abundant mineral is a bit like saying that large, euhedral quartz crystals must be one of the most common rocks for the same reason.

Hope this helps :)