Whether стон is moan, groan or cry, and whether тревожный refers to alarm or even despair depends on the overall tone of the poem.

For example, in the translation of "Sea Fever" by John Masefield, "sea-gulls crying" is described as "чайки тревожный стон."

I must go down to the seas again, for the call of the running tide
Is a wild call and a clear call that may not be denied;
And all I ask is a windy day with the white clouds flying,
And the flung spray and the blown spume, and the sea-gulls crying.


Морская лихорадка
Опять меня тянет в море, и каждый пенный прибой
Морских валов, как древний зов, влечет меня за собой.
Мне нужен только ветреный день, в седых облаках небосклон,
Летящие брызги, и пены клочки, и чайки тревожный стон.
— Перевод С. Я. Маршака

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The first variant harks to the biblical Genesis 1:3:
In the beginning God created the heaven and the earth. And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. And God said, Let there be light: and there was light."

In the second option, "rings" refers to the "ringing sound of an alarm bell" and to the action of ringing (going around, like a ring) the earth.