I understand we should wait for the comments from specialists either in Mongol History or in Maritime Asian History, such as /u/Total_Markage, /u/The_Jackmeister, and /u/_dk. What I can at least do is to summarize the historiographical circumstances and problems on the relevant sources.
AFAIK few academic literature, either in English or in Japanese, or either in Mongol History or in Maritime Asian (or further, Ryukyu) History, mentions the possible Mongol invasion into Ryukyu Islands. Among the references that I can check for this comment (see below), only [Ota 2009] discusses the entries in question.
I suppose the main reasons of their 'negligence', or hesitance to take the account cited in the linked board by OP are threefold:
- Though the historical source mentioned in the linked board is an official history, Chûzan Seikan, it was recorded in the middle of the 17th century, more than ca. three and half centuries after the events. There was no direct dynastic relationship between the Sho dynasty in the 17th century and the (quasi-legendary) dynasty in the late 13th century. In Ryukyu history, the 13th and 14th centuries are called Gusuku (Fortless) Period, characterized by the political turmoil, and we know little about this period for sure in detail, based on the written evidences. It is also worth noting that I personally doubt whether the author of Chûzan Seikan could in fact refer to the History of Yuan to use them as a source of his historical writing (see 2).
- In fact, even the official History of Yuan mention the invasion plans into 'Liuqiu' in the entries of the years 1291-2 and 1297 respectively, but the details might be a bit different from Chûzan Seikan.
- Then, why have researchers hesitated to discuss these entries? The most conspicuous reason is: Most of the scholars agree that 'Liuqiu' in the History of Yuan was probably not exactly Ryukyu (Okinawa) Islands now (Cf. Yokkaichi ed. 2008: 166). While they have not reached an agreement on the exact details, the geographical concept of 'Liuqiu' in medieval Chinese writings seems to be rather vague, encompassing different archipelagoes in Eastern Chinese Sea, such as Taiwan, Okinawa, (and probably Amami and Yaeyama Islands) (Ota 2009: 202-04). Ota argues that most of the Chinese in Yuan period didn't have a concrete geographical knowledge of these islands so that they often say different idlans under the same term, 'Liuqiu'. It was not until the beginning of Ming China that the politically stabilized Ryukyu kingdom established a trade as well as diplomatic relationship with China.
- In sum, the majority of scholars seems to agree that 'Liuqiu' in the history of Yuan history that the Mongols sent the fleet to conquer might well be Taiwan rather than Okinawa Islands. We know very little on the exact diplomatic relationship between now Okinawa and Yuan China in late 13th century for sure.
References:
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- Masashi HANEDA & Mihoko OKA (eds.). A Maritime History of East Asia. Kyoto: Kyoto UP, 2019.. I only refer to the Japanese original, though.
- May, Timothy. The Mongol Empire. Edinburgh: Edinburgh UP, 2018.
- Masaki, MUKAI. 'the Structure and Transformation of Mongol Sea Power (in Japanese)'. In: Global History and Empire (in Japanese), ed. Shigeru AKITA & MOMOKI Shiro, pp. 71-106. Osaka: Osaka UP, 2013.
- Shosuke MURAI. Old Liuqiu: A shining kingdom in Maritime Asia (Original Title in Japanese: Ko Ryukyu: Kaiyo Ajia no Kagayakeru Ohkoku). Tokyo: Kadokawa, 2019.
- Yukio OTA.'Two 'Liuqiu's: how people perceived 'Liuqiu' in the 13th and 14th centuries Eastern Asia (in Japanese)'. In: Ryukyu and Fusian in the 13th and 14th centuries (in Japanese), ed. Shoko KINOSHITA, pp. 201-18. n.p.: Kaken Report, 2009.
- Yasuhiro YOKKAICHI (ed.). Maritime Asian History seen from Material Cultures (Original Title in Japanese: Mono kara Mita Kaiiki Ajia Shi). Fukuoka: Kyushu UP, 2008.