In the case of ContentID, which bypasses the DMCA, yes, they are to blame, along with all the media companies that demanded its creation.

What I don't understand is why someone uploading videos like that isn't being sued for straightforward copyright infringement.

The measures under the DMCA (and similar measures elsewhere, such as under the EUCD in Europe) were supposed to protect YouTube, the hosting service, in cases like this. Otherwise, the host is vulnerable to fallout from illegal acts committed by others and of which it has no knowledge. It's a similar argument to the common carrier principle in other communications channels.

Now, you can certainly debate whether the protection is too generous. For example, under this sort of scheme it is possible to build a business that facilitates and encourages copyright infringement and generates huge revenues as a result of that business model, yet wash your hands of it by claiming to just be the innocent third party host. This is still about the hosting service, though.

As far as I know, none of the DMCA-style laws protect the original uploader who actively and in this sort of case knowingly shares someone else's content in breach of copyright. If they're doing that with the kind of content that picks up millions of views and consequently denying advertising revenues and marketing effects to the legitimate creator/rightsholder, why isn't that grounds for a regular copyright infringement suit and, in a jurisdiction like the US, seeking statutory damages that make it worth pursuing one?