I don't think the criticism is outdated, in spite of what you mention. Indeed, in the last few decades, releasing the code has gone from uncommon to standard practice. But in my view, both you and the post author are greatly overstating the importance of releasing the code. Sure, releasing it is clearly better than not releasing it, it's a step forward. But it makes very little difference to peer review, if at all, since peer reviewers hardly ever actually open the code. You already are lucky if you can find reviewers that read the whole paper rather than skimming through the dense central sections - good luck finding reviewers that will actually check the code, considering that it takes much more time and effort than reading a paper. When I'm myself a reviewer, I also penalize papers with no code - but papers
with code might as well link the Minesweeper source and most of the time I wouldn't notice, because I don't have time to check - and I devote more time per review than most people I know.
Regarding your second paragraph, that is what peer review actually is in the present time, but the point is that it's supposed to be much more than that. And the problem is not only outright fraud that might have severe consequences, the post itself mentions "soft fraud" that will hardly ever have any consequence (who is going to notice that someone made several experiments and only published the one favoring their conclusion?). And there are also problems not related to fraud - for example, peer review is supposed to be not only about correctness but choosing the best work for top-tier venues, good but not that impactful work for second tier, etc. Shallow peer review often means that work that is not fraudulent, but not stellar is accepted in better venues due to famous authors/institutions or just authors that are especially skilled in "pitching" their work, and vice versa.