There have been a few absolutely infamous cases of astonishingly shoddy game developers trying to silence negative criticism of their video games by trying to abuse copyright laws. In other words, the developer tries to remove all negative criticism from the internet by claiming copyright on the material and, of course, abusing DMCA takedowns.
In some cases it has gone to astonishing lengths, such as the case of Digital Homicide pursuing a year-long lawsuit against the video game critic Jim Sterling, for the sole reason that he made negative review videos about their games. The whole process was really long and really ugly, with Digital Homicide, piling up claim after claim, and after they were all dismissed by the court, the main owner of the company transforming it into a personal slander lawsuit, again piling up claim after claim. After about a year he just gave up, and the lawsuit obviously didn't achieve anything.
There's also a very similar copyright/slander/whatever lawsuit made by another company against the YouTube critics h3h3 Productions, and it's equally ugly, nasty, and nonsensical. And these are by far not the only two cases, just the most prominent ones (there have been many, many others, but they have often ended much sooner. All of them in favor of the accused, ie. the video game critic, of course.)
The crucial thing is, of course, that copyright law fully protects critics. Critics have the fundamental right to criticism, and using footage from the work being criticized is explicitly considered fair use.
That doesn't stop some people from trying anyway. Especially on YouTube DMCA is so astonishingly easy to exploit. The only thing that the IP owner has to do is to fill up some online form, and like by magic the video is down.
The thing about YouTube DMCA, however, is that it has a somewhat fair countermeasure (required by law): The person who made the video can make a counter-claim, and have his video automatically restored. In this case the only recourse that the IP owners have is to take the case to court, if they think their DMCA claim was legit. In 99% of cases they don't.
However, a game company has now discovered a new tactic to take negative reviews of their games down on YouTube, which bypasses the DMCA mechanism (and, curiously, they used it against Jim Sterling; seems like he just can't get a break): Rather than use copyright, they use trademarks instead.
YouTube has no policies with regards to trademarks. They are not required by law, or by any statutes, to react to trademark claims, and they have no mechanism to deal with such claims. YouTube could just as well ignore any "trademark claims" they receive with no repercussions, because they are not obligated by any law to react.
However, it seems that YouTube's policy is to react to companies sending them takedown requests based on trademarks. A company sends them a message that "this-and-this video breaks our trademarks", and YouTube will take the video down. Apparently manually. There is no automated system for this.
Likewise there is no countermeasure that the creator of the video can take. There is no system to make any sort of "counter-claim", like with DMCA. The video is down for good. Complaining to YouTube isn't going to help; they won't do anything.
The only recourse that the creator of the video has is to take the company to court, win the case, and then send YouTube the court's decision and hope that YouTube restores the video. And if they don't, the only recourse remaining is to ask the court to demand YouTube to restore the video.
99.99% of people, heck, maybe 100% of people, aren't going to do that. They aren't going to take a corporation to court over a single video, because of a spurious trademark claim, hope they will win, and then on top of that possibly try to issue a legal restoration demand to YouTube.
So it's a perfect scheme, really. It seems that where copyright claims fail, trademark claims are the absolutely perfect weapon to take down negative YouTube video reviews for good. Even though YouTube has no legal obligation to obey such trademark claims, they do. And there's pretty much nothing that the video creator can do about it, other than go through a hopeless and endless legal battle, just to have one video restored.