You can think of these guys as protozoa, if you want. They’re protista (single celled organisms) with the kind of cell structure that makes them eukaryotes (like us) and not prokaryotes (like bacteria). But they’re not plants, they’re not animals, and they’re not fungi.
These particular protista are interesting because (1) they have two nuclei (a macronucleus and a micronucleus) and (2) when they divide, only the micronucleus replicates, the big one has to be built from scratch each time. [Ref]
Phylum: Ciliophora = large, complex, but single celled, with cilia & two nuclei