Hello, unfortunately, I also can't find the app on the store right now, on a new account.
It seems like they removed it currently, I investigated a little bit further on the case.

Their website is still up:
https://dogefaucet.nyandev-id.org/

I contacted them via the eMail address given on that website, but I have to wait for their reply for now.

The only thing you could try is to download the .apk from a third party website like here and install it manually, but I haven't done so myself, this is at your own risk:
https://apkpure.com/dogefaucet-free-dogecoin/org.nyandevid.dogefaucet

The app itself is still functional for me as of now, I just hopped on and tried it.

Sorry for the inconvenience, I'll post here in the comments again if I get a reply from the dev team.