1. Diamond mentioned the rats as contributors to the deforestation; invasive species brought by humans (which the rats were) are a key example of ecological destruction.
2. Going from 9000 (or possibly as many as 15,000) in the 1500s to 3000 (using the most generous pre-disease estimate) at the time of first European contact sure as hell sounds like a dramatic decline to me, and the author doesn't propose how it happened.
The author doesn't seem to give a lot of credit to the locals and their own accounts of history. Those stories are often much more accurate than we think.
Look at Africa, and the civil wars that popped up after post-colonization.
Or, I mean, look at Iraq now. When an outside government overthrows the current power, sets up their own ideal of a government, and then leaves, it usually doesn't end up well, right? There's going to be hangers-on of the old ways, they are going to be a PITA for the new system, once it's set up.
So if there was a drop in population it may not have been as big of a drop as 15,000 to 3,000.
[1] https://www.amazon.com/Enigmas-Easter-Island-Paul-Bahn/dp/01... -- cool book. The title is tongue in cheek; he mostly is annoyed by people who don't simply apply standard archaeology and anthropology to the island and look for more complex theories than necessary.
The author says quite clearly it's not clear that it happened at all: "The question ... is one we still cannot convincingly answer ... But there is no real evidence of a population decline prior to the first European contact". Also you've cherry picked the high end estimate from "4k-9k"; going from 4k to 2K-3K is far less dramatic than 9k to 2k-3k. All of these numbers are pretty shaky estimates and Roggeveen admits his 2-3K estimate may be low as they were shooting people and they did want to line up on the beach to be counted. So maybe it's 5K to 5K.
Diamond's narrative of a starving people forced into cannibalism as a food source certainly doesn't fit much of the other evidence -- their bones indicate they were larger than other polynesians, not malnourished and show little evidence of being killed in battle.
One theory posited by people like Charles C. Mann is that the native population of say, North America were drastically reduced before the likes of English colonizers came onto the scene by infectious diseases.
Maybe, maybe not (and maybe that happened well after)
One consideration (not raised in the article) is that perhaps the people of South America (unlike the Polynesians) did not have the seagoing technology or know-how to make a round trip to the island, prior to the arrival of europeans.
The English were relative latecomers among the European colonists of the americas, and by then smallpox and other diseases had spread widely. Apparently, the Wampanoag had suffered from an epidemic, now suspected to have been smallpox, in the years prior to the arrival of the Mayflower Pilgrims in 1620.