I see the decision to use DDR5 performance data with the 12600K has carried over from the review. At this time, and likely for at least the next year, pairing DDR5 with a 12600K makes zero sense. For less than what it currently costs to go with DDR5 over DDR4, one could move up from a 12600K to a 12700K, and net a larger performance gain than the differences DDR5 brings to most workloads.
And just as concerning for memory performance comparisons is that the Alder Lake setup appears to get the advantage of dual rank memory dimms, whereas the other platforms are restricted to single-rank dimms at half the capacity, which can in many cases make more of a difference to performance than the RAM's timings alone. Pairing the 12600K with DDR4 and using 32GB kits with all platforms would make for a more meaningful comparison. The performance differences would still likely be minor, but when we're considering a few percent difference to be a win or a loss, all hardware should at least be compared on equal footing, or at least as close as possible.
The 5800X is an 8-core processor. Also, it hasn't been anywhere close to $150 more expensive for quite some time. Typical sale pricing at US online retailers has continuously been under $400 for the last five months, since mid-June, and it has at times seen sales as low at $370. So around half the price difference you are suggesting. And that's just the processor itself. Factor in the currently higher platform costs for Alder Lake, and even with a DDR4 build you are looking at a similar total cost between the two builds. And a 5600X build can cost less, so it's only natural that the 12600K should perform better, especially since the Ryzen 5000 series has been on the market for more than a year at this point.
Pricing will naturally need to drop further though, as more competitive locked processors and motherboards should be coming early next year, and I would expect to see larger sales on these processors in the coming weeks, since AMD can easily sell them for significantly less while still turning a profit.
While I agree that showing minimally-restricted CPU performance by running games at a low resolution on the highest-end graphics hardware can be useful to highlight small differences in performance, at that point the tests become synthetic benchmarks more than anything. They can potentially hint at performance differences in future, more demanding games years down the line, but nothing is guaranteed at that point.
In any case, this isn't a CPU review, it's an article purporting to provide a real-world comparison of performance, features and pricing, as they stand today. And in real-world scenarios, outside of relatively niche, heavily-multithreaded workloads like CPU-based video-encoding and rendering, the performance of all of these processors will tend to be indistinguishable. And while I would say AMD's pricing is in need of adjustment, the situation isn't anything dire like the clickbait title "Ryzen Has Fallen" might suggest. In general, I'm never particularly fond of these "versus" articles, as they tend to be little more than a rehash of review data, and almost always make poor decisions when simplifying the content into a table of wins and losses.