We have found two possible interpretations of this phrase.

First interpretation

The first and more immediately obvious meaning of “Portés a terre” is
that something, possibly the waves of the sea, have brought the three
survivors of the accident to dry land after the ship was destroyed.

This is apparently the interpretation of the English translation of the novel from 1874, Philadelphia, J. B. Lippincott & Co., available digitized in Project Gutenberg, which translates the sentence of the message in chapter 3.21. as “Carried by the waves, two sailors and Captain Grant reached Tabor Island”.

My main problem with this
interpretation is that it seems to be redundant with the last part of
the sentence, “ont atteint à l’île Tabor”, which also tells that the
survivors have reached the land. (In that last part of the sentence,
“atteint à” is an idiom meaning to reach something with difficulties,
as you can see under the heading “atteindre à” in the Wiktionary
definition of “atteindre”.) However, Verne may have introduced
this redundancy to forward the plot, for the phrase “à terre” appears
in the surviving fragment of the English copy of the message as
“aland”, and that is the main clue leading the heroes to New Zealand.
Another problem with this interpretation is that it doesn’t completely
match the story Captain Grant recounts: “nous parvînmes à gagner la côte après vingt tentatives infructueuses” (we have succeeded to reach
the shore after twenty failed attempts).

Second interpretation

The second possible interpretation is that the survivors have chosen
to head to the direction of the shore, likely also after the
destruction of the ship. This interpretation is based on a rarer
meaning of the verb “porter”, given as definition 28 in the
Wiktionary definition of the verb.

The main problem with this interpretation is that this would require that the three survivors the subject of “porter”. That makes the grammar of the sentence strange, for it seems from it that the survivors are the object of “porter”. Although Paganel argues in chapter 3.19. that Captain Grant need not have had perfect command of the French language (“[le document] a été écrit par un Anglais, auquel les idiotismes de la langue française pouvaient ne pas être familiers”), Verne would probably not use this as an excuse to put a sentence with wrong grammar in the message, especially as the word “portés” isn’t constrained by the fragments.

This is the interpretation Lord Glenarvan guesses in chapter 1.2. when he reads the fragments of the message, reconstructing the phrase as “Se dirigeant à terre”. Given that Glenarvan only had the word “aland” to start from, that hardly proves anything, except for that Verne saw this as something plausible to write in a message calling for aid.

Remarks

I would further like to mention that another public domain translation to English (unknown date, ed. Charles F. Horne, Ph.D., available from Project Gutenberg) does not translate the real text of the message at all in chapter 3.21., quoting it only in French (with a typo). A Hungarian translation by Bartócz Ilona (1983, Kriterion, Bukarest, text available from MEK) does translate the message, but the translation isn’t close enough to the original to prove anything: “Két matróz és Grant kapitány partra vetődött a Tabor-szigeten.”

Conclusion

Taking all the findings so far, I find the first and more obvious interpretation more likely, but I could be convinced otherwise. If you know what the interpretation is (you don’t need to stick to these two), or have more evidence, please post an answer.

Pour une analyse plus fine d’un mot, il faut le replacer dans son contexte pour éviter toute confusion.

Extrait du texte original :

— Mylord, le voici mot pour mot, répondit Harry Grant.

« Le 27 juin 1862, le trois-mâts Britannia, de Glasgow, s’est perdu à quinze cents lieues de la Patagonie, dans l’hémisphère austral. Portés à terre, deux matelots et le capitaine Grant ont atteint à l’île Tabor…

— Hein ! fit Paganel.

Basemetal a répondu à votre question dans le lien que vous avez proposé.

En effet, après un naufrage la mer "porte" l’embarcation de fortune des rescapés qui dérive du fait de la houle et des vents.

Ainsi les rescapés sont portés à terre (sont poussés vers), expression de marine comme : le vent porte au large (emporte avec lui).

En marine, porter signifie aussi une direction : le bateau porte à bâbord, il a tendance à se diriger vers la gauche (en général sous un vent de tribord amure qui fait dériver le navire), c’est-à-dire que le trajet du bateau est orienté plus à gauche que l’axe de la quille.