I can't find any reference to such a statement by Chiang. There was an influential fascist clique within the KMT modeled on Mussolini's Black Shirts, and irredentism was a key factor in Chinese politics of the day- but the islands of the South China Sea were not of prime importance or significance at the time that the 9-dash line was first announced. They were, however, the subject of a long-running but low-intensity dispute.

The Republic of China accepted the surrender of Japanese forces in the South China Sea in 1946 and afterwards published a map bearing the famous dashes around the region in 1947. At the time the legal status of the islands was ambiguous, with China and Vietnam having disputed much of the area throughout the 19th century and subsequently France having taken up the now-colonized Vietnam's claims in the 1930's.

The UN Convention on the Law of the Sea did not begin until 1973, some 25 years after the line was first publicized, so while we can view the PRC's contemporary use of the claims as a rejection of UNCLOS, at the time that Chiang Kai-shek's government first made these claims they do not seem to have been in violation of contemporary standards of international law, representing instead a bilateral dispute between China and Vietnam (at that time still a French colony).

In light of the geopolitical context, it appears that the ROC government was looking to capitalize on Japan's surrender to put an end to a dispute that had by then already been going on for half a century. This article is making massive leaps in assuming (1) that the declaration was made directly on the orders of Chiang Kai-shek (2) that Chiang was motivated by expansionism in stating these claims and (3) that Chiang embraced expansionism out of admiration for Nazi race theory.