Die See denominates the abstract concept sea instead of a specific sea (except, of course, proper names like Nord- and Ostsee). The concept is basically the entirety of the seas. You have a lot of idioms like raue See, auf hoher See, in See stechen and so on, but you can not really say Ich bade gerne in der See or Ich gehe auf der See segeln (note: der See = dative here). That's already too concrete and requires the noun Meer.
As you say, as a abstract noun denominating an unique concept (there's only one entirety of seas), die See does not have a plural.
The example you give could be a wrong translation. It features at least another error (um ihnen herum instead of um sie herum). But most decisively, it doesn't make sense here because there aren't literally multiple seas around them.
Especially, there is no traditional usage of die Seen (f. pl.). As DWDS states, the differentiation happened quite late in literature, so you wouldn't find a medieval source about the vikings, for instance, talking about die Seen:
See ist ursprünglich Maskulinum. Schwankungen zwischen maskulinem und femininem Gebrauch bestehen im Aengl., Mhd., Mnd. und Mnl. Der im Dt. an das Genus gebundene Bedeutungsunterschied wird erstmals bei dem Pommern Kantzow (16. Jh.) deutlich, aber in der Literatursprache erst im 19. Jh. voll ausgebildet.
Die See really doesn't have a plural and since it is denominating one unique concept, it isn't clear what the plural would be.
Edit: There is another meaning of die See which @tofro points out.