"Do you know the meaning of that word?"
It's not that 知ります doesn't exist, it's just that it doesn't mean "I know" as a present-tense declaration of the state of things.
A Japanese speaker on that page gives this example:
"It is upon losing something that a person knows (comes to know) the importance of that thing."
The te-iru form is being used to describe the state of knowing. Having learned something, one continues to know that thing until they forget it, so that state of knowing is described in Japanese using the continuous aspect (te-iru form). However, the continuous aspect in English (knowing) sounds awkward here, so the simple aspect (know) is used instead.
Technically, the English simple overlaps with the continuous. Someone watching a bird flying could say "That bird flies so gracefully" or "That bird is flying so gracefully" and both sentences would be mostly synonymous despite one using the simple and the other using the continuous.
知る and 知ります, however, use the imperfective aspect, which is also exhibited in English by the simple form. The verb in this aspect is used to express the process through which one comes to know things, rather than the act of knowing itself. So it is often translated as "to learn", "to experience", "to understand".
"It is upon losing something that a person learns the importance of that thing."
Usually, these senses can be described with other, more common verbs, so you don't commonly see 知る or 知ります used, but they can be correctly used; they are not forbidden or archaic or unused. The confusion here comes from the difference between the English simple and English continuous compared to the Japanese imperfective and the Japanese continuous.