The link that you provided pretty much gives the answer to the question. There are two factors:
- The quality of the coin. The Canadian Gold Leaf, for example, has at least 0.9999 fitness, so it's extremely pure. Very pure coins are of sufficient quality to fulfill commodities contracts as gold rather than as coins.
- As you suggested, the age of the law also seems to matter. From your link: "Many exempt products, like the American Silver Eagle coins, are not on the [exempt] list because they were not in existence when the Reportable Item list was created."
EDIT with a bit more info:
Under 26 CFR 1.6045-1, gold and silver bullion of a certain quality and at minimum quantity are effectively defined as commodities subject to reporting since, at the minimum quality, they can be delivered to complete regulated futures contracts. The default treatment of such commodities is that sales should be reported, but there is an exception for foreign currency. That seems to be why most foreign currency coins are exempt.
That leaves the question of why a few are specifically reportable. I couldn't find the IRS ruling that lists those that are reportable. The US, however, started minting gold coins in the late 70s pursuant to the American Arts Gold Medallions Act of 1978 (Title IV). (https://www.gpo.gov/fdsys/pkg/STATUTE-92/pdf/STATUTE-92-Pg3641.pdf) Although this article (http://lawdigitalcommons.bc.edu/cgi/viewcontent.cgi?article=1564&context=iclr) is primarily at about taxation by states, it claims that
The Act has two main objectives: (1) to permit U.S. citizens to buy and hold gold for investment purposes in relatively small amounts; and (2) to compete with the Krugerrand and other foreign gold coins, so that less gold is imported into the United States and fewer dollars are exported.
I read the relevant part of the Act, and I didn't see a list of specific coins reportable. (For that matter, I'm not sure that Form 1099-B as we know it today even existed at that point in time.)
Finally, if you check the coins on the "reportable" list in the OP's link, I think that you'll find that most have no face value as currency. (The Canadian Gold Leaf has a face value and so do the US coins. The others seem to only have value based on their metal content.) I couldn't find anything specifically stating that's why they are reportable, but I did find controversy in a couple of respects about whether these are actually "currency" under U.S. law and whether the designation might depend on which part of the law is at issue.
I don't have time to dig further than this, but it's at least some anchor to law and history to support my answer. If someone has something more definitive, I'd be interested to see read it.