Was this really DMCA? The article implies it is, but I don't see any evidence (maybe I missed it). There is discussion of what the DMCA says, and Google took the article down. However it is generally understood that DMCA rarely is used to take things down. Instead Google has a "I can't believe it isn't DMCA" process that looks similar, but in reality it isn't actually DMCA.

If this is really DMCA then the author should press charges - DMCA take downs are done under penalty of prejury which is a criminal act. Since author legally has copyright they have legal protections under DMCA for exactly this.

If this isn't DMCA then it is just Google decision not to index something. They have the right to not index anything they choose not to. Nothing the author can directly do about this - but indirectly they can be witness that Google isn't a "common carrier" since they choose not to index that wasn't copyright, so you just need to find some case where someone else sues google because they found something "harmful" (likely something like suicide instructions)