It is right there on the Eurasia map at the link you shared, and on the list of Eurasian territories, so OP was correct.
The thing is that “continental Europe” is not the same as the continent of Europe, which does include the islands. Mainland Europe is a less ambiguous name.
The largest Eurasian islands by area are Borneo, Sumatra, Honshu, Great Britain, Sulawesi, Java, Luzon, Iceland, Mindanao, Ireland, Hokkaido, Sakhalin, and Sri Lanka.
It is right there on the Eurasia map at the link you shared, and on the list of Eurasian territories, so OP was correct.
The thing is that “continental Europe” is not the same as the continent of Europe, which does include the islands. Mainland Europe is a less ambiguous name.
Yep, it’s part of the continent.
Also the Islands section of that page says this:
(Emphasis mine.)