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Tamgusuku was a `king` of the Okinawan kingdom of Chūzan from roughly 1314-1336. He was the third son of Eiji (r. 1309-1313), he was the fourth ruler of the lineage of Eiso (r. 1260-1299).Tamagusuku lacked the charisma and leadership skills to command respect and loyalty from those lords (the anji). A number of these lords rebelled, and the island of Okinawa came to be divided into three kingdoms. Tamagusuku, remaining in Urasoe, became king of Chūzan. His failure to institute reforms or innovations in governance is generally claimed as one of the causes of the fall of the lineage (dynasty), which ended with Tamagusuku's son and successor Seii.[3]

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That's all i know from wikipedia

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that link does not answer the question completely it leads to another link that says the following;

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There is no consensus about the etymology of gusuku. Chamberlain analyzed the word as the combination of gu (< honorific go 御) and shuku (宿). Kanazawa Shōzaburō also segmented gusuku into gu and suku but considered that the latter half was cognate with old mainland Japanese shiki, in which ki was a loan from some Old Korean language. Iha Fuyū proposed that suku was cognate with soko (塞, fortress). Hirata Tsugumasa considered that suku was cognate with mainland Japanese soko (底, bottom).[4]

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Higashionna Kanjun raised doubts over the analysis of gu since older records always used honorific u (< o) instead of gu (< go). Nakahara Zenchū identified gu as go (stone)

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As for the first part, Tama is easier to find, it means ball, sphere, globe, orb, bead (of sweat, dew, etc.); drop; droplet, something round.

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so far that under certain theories that adds to "round spherical stone", but nothing so far is certain, alternatively, "round spherical/semispherical/cylindrical fortress" or "round territory" (a gusuku is a kind of territory).

You'll find information on Tamagusuku at http://en.wikipedia.org/wiki/Tamagusuku_Castle.