Are you always this hostile, or just to random people whom you have never met?
Anyways...
What I should have said is that you can copyright a presentation/display of facts, assuming it is "fixed in a tangible medium of expression", and that copyright gives you exclusive rights to that particular presentation. However, the facts themselves don't become copyrighted merely because they've been fixed in some form. Therefore, the fact that someone else has "fixed" the moves on a website, video recording, or cuniform table is irrelevant. Incidentally, the phrase "fixed in a tangible medium of expression" is important because it is literally the wording of the law.
When I wrote arrangement, I was imagining something like the layout of a table. If you, for example, generated a little diagram showing how the board changed after each move, those diagrams would be copyrightable, since you've arranged them in a specific creative way (you chose these icons, that layout, etc).
The arrangement of the data in a broader sense (i.e., curation) can make it copyrightable, but it has to involve some element of curation. For example, in Key Publications, Inc. v. Chinatown Today Pub. Enters, the Court held that a curated list of businesses (in this case, businesses that were thought to be especially support of or relevant to a Chinese-American community) was sufficiently creative to be copyrightable. However, the bar is low, but it is not zero. Under Feist, an obvious arrangement (alphabetical order) was not original enough for protection. I would argue that putting a sequence events in the order that they occurred is much closer to Feist. In fact, I'd argue that any other ordering would actually be closer to copyrightable (e.g., "Top 25 Chess Blunders of 2016").
The obvious counter-argument, which you seem to be making, is that if you're allowed to list facts in some naturally-occurring order, then you shouldn't be able to copyright anything, because you can just spam out a description of the contents: "An audio file containing "War Pigs" by Black Sabbath, when encoded using the default settings for libFLAC, starts with 3 frames of silence. This is followed verbatim block containing the following values....F"
These are facts, literally speaking, but they're vacuous. No one would be interested in them absent an attempt to reproduce the underlying work whose copyright you're (not) avoiding infringing. In contrast, the moves made during a match are of more general interest. This is a admittedly a grey area, but it's not particularly grey--maybe it's more off-white--and the law is full of grey areas and judgement calls.