The "baubles" referred to in this story are the silmarils, created by Fëanor in Valinor. They were stolen by Morgoth when the vala killed Fëanor's father Finwë, and Fëanor and his sons (including Maglor) swore an oath to reclaim the silmarils. This was actually what drew them to Middle-earth.
The Fëanorians made war against Morgoth but finally it became clear that this war was hopeless, and so the brothers let the matter rest. After Beren and Lúthien took the silmaril from Morgoth, the Fëanorians attacked the Elven kingdoms that held the silmaril, events that became known as the Kinslayings. The silmaril was passed to their son Dior and finally his daughter Elwing, who carried it out of Doriath to Sirion. After a time the Fëanorians learned that the silmaril was in Sirion, and so they attacked that settlement in what Tolkien described as "the last and cruelest of the slayings of Elf by Elf" ("Of the Voyage of Eärendil," The Silmarillion).
The encounter between the Telerin youth and Maglor is my own invention, but the attack on Alqualondë is not. The Fëanorians needed ships to travel from Valinor to Middle-earth and did not have any of their own, and the Teleri shipbuilders refused to give them ships since they were leaving Valinor against the wishes of the Valar. The Fëanorians tried to steal their ships, and the conflict escalated into an all-out battle. The Fëanorians then burned those boats they did not need to keep the other Noldor from sailing with them to Middle-earth. This is the "ships burning" that Maglor remembers.
I hope this helps you understand the context of this ficlet better, if you did not understand it already.
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