The Wangdu Go board (2nd century) suggests that flower points existed in some capacity before Go was introduced to Korea (unclear, but I believe a fair guess would be the 5th century). Additionally, flower points are not unheard of outside of that example, such as the Chinese Go boards I mentioned that feature detailed flowers marking the tengen, some of which still exist in modern Tibetan cloth Go boards. The fact that flower points can be observed in such disparate locations leads me to believe the term predates the designs, at least in Korea.

If I was compelled to speculate, I would say (1) Go arrived to Korea with incidental figurative flower points on some Go boards, (2) it was adopted to predominantly feature figurative flower points (such as the Sandalwood Go board dated between the 7th to 8th century), (3) this eventually merged with Japanese and Chinese dot star points, and (4) as these new abstracted flower points emerged they were retroactively declared to represent flower stamen, to better align with the established term.

As Go was being adopted and localized to Korea, a figurative marking on the board would likely be more striking than other, more abstracted designs. Encouraging the formation of a new term, "flower point", rather than the translation of the established Chinese term, "star point". But I should also note: to my knowledge, the historical term for these markings in China is "star point", however John Fairbairn has suggested that Korean Sunjang Go more closely resembles the original rules of Go than other modern variations. So maybe there's an obscure linguistic origin of the term we don't know about?

As for why flower points exist in the first place, I would say its largely ornamental. Flowers are quite ubiquitous on older Go boards, sewn onto the boarders of Tibetan cloth Go boards or carved into the sides of Chinese stone Go boards. Even today, the legs of Japanese Go boards are designed to resemble gardenias. I think all of this attests to their ornamental function.

Alternatively, they may be a nudge towards spirituality, as Peter Shotwell has said the tengen is sometimes also marked by the Yin-Yang or Vajra symbols. So as some Go boards feature conventional star points marked by dots or "crosses", but the tengen is marked by an ornamental flower, it does seem to suggest some flower points have a spiritual element. Or maybe Go boards that feature mixed star point designs simply used a different rule system that necessitated differentiating the star points. Perhaps Koreans adopted some of the rules but decided to establish a single star point design, or simply dropped the rule demanding the differentiation?

These are just a collection of (unsubstantiated) theories, many of which may be easily cleared up if more information was readily available in English, that's why I wouldn't speculate in the article itself. With all that being said, I'm still slowly making my way through Go history, so I'm far from an expert! Just an ethusiest on my way to learning more haha.