I think the [^[] was making the start-of-line/string optional

*scratch*.el

(let ((regex
       (rx 
        (or bol bos)
        (? (not (any "[")))
        (group
         (>= 2 (and (any "A-Z")(one-or-more (any "a-z")))))))
      case-fold-search)
  (list
   (replace-regexp-in-string regex "{\\1}" "[OneWordOrMore]")
   (replace-regexp-in-string regex "{\\1}" "Onewordormore")
   (replace-regexp-in-string regex "{\\1}" "[OneWordormore")
   (replace-regexp-in-string regex "{\\1}" "OneWordOrMore")
   :regex regex))

;; gives ("[OneWordOrMore]" "Onewordormore" "[OneWordormore" "{OneWordOrMore}" :regex "\\(?:^\\|\\`\\)[^[]?\\(\\(?:[A-Z][a-z]+\\)\\{2,\\}\\)")