"Although Buddhism seems so different from religions like Christianity and Islam that it doesn't look like it should be in the same category, it still shares with other religions a very basic element: a belief that the universe is in some fashion set up for our sake — or at least set up in a manner conducive to our needs. In Christianity this is more obvious with the belief in a god that supposedly created the universe for our benefit. In Buddhism, it is expressed in the belief that there are cosmic laws that exist solely to process our "karma" and make it possible for us to "advance" in some fashion"
Ummm, ok? I don't understand why he, and many others, try to pigeon-hole all Buddhists, or better yet all people into little different boxes, wrap them up with neat little bows and then proclaim them all wrong, without first seeing or exploring for themselves. I have quite a few self professed atheist friends, including my brother, who are open to the notion that maybe the world isn't black or white, who understand you can't always define every little aspect of reality and who want to see for themselves rather than relying on what someone else says for truth. I greatly admire and respect this trait in those that claim themselves to be Atheist or Agnostic. God or no God, this is the blunder, to think we rely on belief or some holy word or any other extreme view to seek or know truth.
"Although it's more of a problem in some and less of a problem in others, it's still a fairly consistent problem that people are falsely taught that there is something in or above the universe that has picked them out for special protection and consideration."
True enough for most religions, but who told you modern Buddhists are taught this or believe this? If you really think progressive Buddhists think they are picked for some special purpose, then dare I say, you didn't ask any progressive Buddhists? Hell, I may go even as far to say you have a strong opinion about religion itself, as do I, and fit your ideas to match this opinion.
"Our existence is a product of luck, not divine intervention, and any improvements we achieve will be due to our own hard work, not cosmic process or karma."
First off, Luck? Really, luck? Cause God and luck are about the same to me, both words with no real meaning, extreme views on opposite ends of the spectrum. If you believe in luck, why not just believe in a random God, they are both still some belief to be beholden too. Maybe, if you took some time to understand the nature of 'self' you would see ultimately our 'existence' is a product of our own minds. Karma is nothing more than action or cause and effect or as the Buddha said part and parcel to dependant arising. This means we do not exist in a vacuum, but are connected to everything else that is. Time is illusory, and to think things exist as separate objects is the same as the extreme belief of creation or nihilism or non-existence.
"People can try to eliminate these aspects of Buddhism, but they are likely to eliminate so much that it's hard to call the leftover very Buddhist."
You are absolutely correct, I am not a Buddhist; but at the same time I am a Buddhist. If you can see for yourself some truth or logic in this paradox, you will see why we find what is 'left over' to be so valuable.