At no point does the article say that the 13700K ties or beats the 7800X3D in gaming performance. The article says the 7800X3D is the "fastest gaming chip in the world/on the market/money can buy" seven times. (That's just with a quick ctrl-F, there might be more mentions).
In fact, it even says the 7800X3D is the "fastest gaming chip money can buy" in the next sentence below what you quoted above, right there in the gaming verdict section — but you left that part out of your copy/paste. Accidentally, I presume.
The 13700K gets a check in that category because we have three chips in the faceoff, and one of them is far superior in one area but more lacking in another. For example, the 7800X3D is 14% faster than the 13700K in gaming, but the 13700K is 55% faster in threaded and 22% faster in single-threaded — percentage-wise, those losses in productivity are much larger than the 7800X3D's win in gaming.
In other words, proportionately, you lose more performance in applications than you gain in gaming. And that is fine; that is what the chip is designed to do.
As such, the idea is that the 13700K is for people that need a more balanced chip as an alternative in this price class, but still want solid gaming performance. The 13900K is definitely not that chip, as it is overpriced. In contrast, as the words in the article say multiple times, the 13700K is an all-rounder alternative to the 7800X3D that is slower in gaming overall, but competitive on a dollars-per-fps basis and also has a lower overall cost of entry.
Perhaps the text is not clear enough. It also appears that most here have not read the article, verdict section, or conclusion, all of which say these things repeatedly, instead just opting to look at the bullet point. I will add an 'all-rounder alternative' tag to the bullet point in an attempt to make it more clear.