It doesn't sound like they used the DMCA at all. They used copyright takedown requests across various platforms. They never actually filed a DMCA complaint.
You could argue that those takedown requests only exist because of DMCA, but they should exist, regardless of the law.
The problem here wasn't even that this company filed the takedown requests. It's that Youtube/etc complied with them when they shouldn't have. And to make it worse, blamed the victim and refused.
That is, until Forbes got involved and made it higher profile, and then Youtube looked at all of it and realized the mistake.
There's nothing here to indicate that this situation won't continue to be the norm for takedown requests, though. They haven't apologized or said they'll improve their processes. They just swept it under the rug.