Does the chinese letter mean the number, one?
Yes, it is chinese number one. For the whole phrase, it is normally used like 改编自XXX同名小说, means "edited from the novel with the same name from XXX"

0 1 2 3 4 5 6 7 8 9 10 as Arabic numerals。

〇一二三四五六七八九十 for normal use in China (since ancient china).

零壹贰叁肆伍陆柒捌玖拾 for financial use in China, like accounting or bank transaction application.