The quote actually WAS from eorzeapedia, but only because it's easier for me to quote a sentence in good English than trying to write my own.
About Eorzea being a continent in the first quote: That's actually wrong, I'm sorry for posting that, seems like I didn't read it attentive enough.
There's no actual explanation about what Eorzea is in the English lore, but it is in the German localization:
"The map shows the small continent of Aldenard and it's surrounding islands. The entire area shown here carries the name of 'cultural area Eorzea'. All Eorzeans share the religion of The Twelve, but in each city-state another god is worshiped as a patron."
So basically, Eorzea is a cultural region, meaning the culture and lifestyle has to be very different on the other continents.

Ala Mhigo still belongs to Eorzea though, because even though people there have been brainwashed by the Garlean Empire for years, their lifestyle, religion and technology are still the same.
That's what some NPCs say, although we could also start a discussion about how to judge the knowledge of NPCs..they could just be wrong.

After all, culture is always tied to a geographical region so it's not really wrong to call the continent Eorzea either.
By definition a continent can't include an island, but when people(NPCs) talk about Eorzea, they don't really think about the culture. They think about the boundaries of the land, like the sea or mountains.
Everything below Garlemald is "Eorzea" to them, even regions which do not have any "culture" at all because no one/only beastmen are living there.
Actually, if we really use "Eorzea" in a cultural context, like it is used in the lore, it may be wrong, because Beastmen already have a totally different culture and different religion although they live in the same geographical region.