I agree with the other posters that these videos are likely to cause confusion to the average viewer, and are probably in violation of trademark law. That said, the way to handle that is in the courts.
DCMA takedown requests only apply to copyright infringement, not trademark law. It is a violation of the law to use the DCMA this way, both according to the USPTOs guidelines(See B.4), and existing case law.
From the article, it is unknown whether their lawyers sent a DCMA request or a some other sort of cease and desist letter. But either way, Digitalocean had no legal obligation to take down the content, or any legal liability if they didn't take it down. The fact that they shutdown an entire service over a toothless complaint about one page on that service is unacceptable, and people should seriously reconsider doing business with them in the future.