I don’t think the article meant taking the mainland of Alaska from Attu. Obviously not, Attu is a looong ways from the mainland of Alaska...at least a thousand miles away, maybe more, I’d have to look at a map.
I think it meant Attu was to be the first stepping stone of taking the Aleutian chain, once the Aleutian chain was taken, they were to be the base for taking the mainland.
Even if the Japanese had taken the entire Aleutian Chain & gotten ashore in Alaska, I doubt that they could have accomplished anything. There were few roads suitable for moving inland or down the coast. Part of the campaign to defend Alaska involved a joint US-Canadian highway construction project that would allow defenders to move up supplies & men.
I think that the Japanese move into the western Aleutians was mostly defensive. They were well aware that the US was planning to sage long-range bombing raids against Japan from these islands. As it turned out the B29 raids came from China, then Guam & Tinian. There wasn’t any need to fight the elements in Alaska. We’d already lost so many aircraft up there.