It's like using the fact that apples fall from trees as evidence for gravity, but because we plan to use gravity to show that time doesn't exist, we refuse to grant that an apple on the ground was ever previously on the tree, but no matter, we still believe in the concept of "falling." In fact, the principles of falling show us that down is better than up, independent of time.
What I appreciate about the article is it grapples with this deep question (albeit framed oddly): When we model the fabric of reality by inventing quantum mechanics, are we somehow just projecting the building blocks of how we think? This is related to another mysterious question: Is math an invention or a discovery? Were prime numbers and linear algebra there before we came along, or do they emerge from the structure of our brains? There are primitive tribes of humans who have not invented counting, so they are unable to distinguish 10 berries from 11 berries and do not experience integers as part of the natural world; they would probably consider properties of the integers to be properties of the act of counting if they had a mental framework for doing so. So back to the first question, how much of what we find when we peer out into the universe and model it with particles and waves and math is in our heads, and how much is really "out there"? If physics to date is unknowingly identifying the fabric of reality with the fabric of thought, then we should be able to take either reality or thought as primary and use it to explain the other. The author chooses thought (consciousness) as primary.
However, the author's claim that objects aren't really there turns out to be more provocative than substantial. The author takes conscious agents as the building blocks of reality, and the conscious agents are still there when you aren't looking. They are just a different representation. You can replace the term "conscious agent" with anything. The author fully acknowledges both of these facts in his responses to objections 1 and 6.