tl;dr 4 articles were published, 6 of them rejected as irreparable bullshit, 7 were rejected but were told would require heavy revision before publishing. As well, they accomplished this by effectively shotgunning massive amounts of bullshit at a large number of journals. Congrats, they've shown that basic social engineering attacks are still effective if you make enough attempts at them. In further scientific revelations: Water Wet, Gravity pulls down, Fire hurts.
Every single research journal*is predicated on A the idea that people are submitting in good faith and B that the journals should pretty much never make decisions on if the material submitted is accurate. When a journal judges content, it is looking for 1: Is the paper well written 2: Is the experimental model described in the paper good and 3: is it relevant to the topic of the journal. It's not the journals job to decide on the accuracy or applicable of what it publishes outside of those grounds, it's job is to disseminate those results to the scientific community, which then collectively decided on the validity. You'll notice that almost immediately after these papers got through, there were multiple sources raising concerns about them, at which point their "experiment" fell apart.
It is not that hard to fake a semi plausible experiment, especially if you go to the extent that these people did by completely and utterly falsify their data. Even in cases where the methodology is imperfect, the fact the result that exists at all can still be of interest. It can guide future research, it can encourage people with better resources to reattempt the experiment. A paper is not published because it is some great light of absolute truth. What a paper says is "this is what we found, this is how we found it, do with that as you will". and they usually do that by examining a special case that can, maybe give light on the more general case. Most papers never lead to any sort of scientific consensus and are usually forgotten.
Because of that expectation of good faith, peer review is an imperfect watchdog for malicious attempts to publish like this. Some people are better able to sniff out bullshit. Different people doing peer review look for different things. Two people may take a look at the same results and disagree with them, however one may take a hard line and shoot the paper down, the other may take the balance of probability and decide that while they don't believe the conclusions are accurate, there is insufficient reason to dismiss them. Nobody doing peer review is looking for "This paper was completely and utterly faked" because down that path lies madness.
Like anything else, if you make a concentrated attempt to bullshit hard enough and spread that around far enough, you will eventually get some of it though. Given enough time and given enough attempts, something will inevitably sneak through the cracks. This is true of everything and is pretty much the most basic form of social engineering based attack on any system.
For this "experiments" conclusion to hold any water, what would need to be shown is that there is a conspiracy to fake results (Pro Tip: there isn't), that these faked results are widely cited and taken as foundation (They don't exist in the first place) and that no one has spotted the issue. Instead what the experiment shows is that by and large the process of filtering bullshit works, and what limited bullshit does make it through is swiftly recognized and called out as bullshit and ridiculed to such an extent that their entire experiment was almost immediately derailed. It shows the exact opposite of their conclusion.