DuckDuckGo certainly has benefited from privacy becoming more salient, but this ruling is probably negative for them. Each of these removal requests needs manual review to keep people from requesting takedowns of other people's stuff. There are ~500M people eligible to request takedowns under the ruling, and if 1% of them ask for one link removed per year that's 14k requests per day. If each request takes 5min then you need 143 people working full time. Which high but doable for Google, but at ~20 employees this would be an enormous burden for DDG.

These numbers could be higher if someone puts out a campaign that goes viral and gets lots of people submitting requests, and there's nothing that stops people outside the EU from submitting (invalid) requests.

One thing in DDG's favor, however, is that that at first people are probably only going to send these requests to Google.

Disclaimer: I work for Google, on open source software.