Strikes are not perfectly 1:1 with DMCA requests. I don't know how to prove that, but I don't trust some reductive Google support pages to have the whole picture either.
I'm fairly confident in what I've said (there's content ID claims, both manual and automatic, and then there's DMCA claims). The EFF does not mention any third option. They mention ToS issues, which are strikes but which aren't because of copyright. And there's a brief mention of contractual obligations, which I mention in my post as well. Those aren't a separate way to take down content, but rather an agreement not to consider disputes from certain rights owners (as far as I know, the only one that's been identified is UMG). This is rare and I have not heard of widespread abuse of this.
It's somewhat confusing because Youtube doesn't always use the term DMCA in their documentation. But it's fairly clear when they say "formal notice", mention that it's a legal requirement, and link to the counternotice page.
You are probably right about all takedowns being done through DMCA. I wish Google was more clear about it.
Your Reddit guide was very good but I would still not call a strike the same thing as a DMCA notice. YouTube doesn't have to have a strike system, they do that to placate the major rights holders who don't want to deal with serial offenders so that there's not a big court battle about whether YouTube knows they are uploading copyrighted content. ContentID serves the same purpose, to shield YouTube from liability. But YouTube lets copyright holders abuse these tools and so far has gotten away from trouble for doing so.
Strikes are not perfectly 1:1 with DMCA requests. I don't know how to prove that, but I don't trust some reductive Google support pages to have the whole picture either.