It's somewhat touched upon but not addresed directly in the video. So here's the answer.
I looked into a few examples of elements named after Western people, like Einsteinium, Bohrium, Copernicium (more at https://languagelog.ldc.upenn.edu/nll/?p=18877 ) and found this general pattern:
The Chinese naming is phono semantic. The radical part of the character reflects the physical property (e.g. "metal") and the phonetic element that sounds like the element's international name.
Take Bohrium, for example, named after Neils Bohr, the Chinese name is 𨨏. The radical part on the left, 金, indicates "metal." The phonetic part of the right, 波, is pronounced "bo" in Mandarin, close enough to the start of "Bohrium."
Another example, Oganesson, named after Yuri Oganessian, the Chinese name is 鿫. The radical part on the top is 气, indicating "gas." The phonetic part below, 奥, is pronounced "ào" in Mandarin, close enough to the start of "Oganesson."