Is there more evidence to show the relationship between 玩 (U+73A9) and UK-20131, other than having the same components 玉 and 元?

There is no evidence that UK-20131 is a variant of 玩, and I very much doubt that it is related to 玩 ("similar to" just means that there is a graphical similarity between the two characters). As a person's name it is more likely to have been read as yuán.