Does Monocercomonoides still meet the definition of a eukaryote? Why or why not?

Yes

Explanation:

They are a unique type of eukaryote because they lack an important organelle: mitochondria. Mitochondria are essential for producing cellular energy in most eukaryotic cells. However, due to its habitat, it is able to acquire energy from a process called  sulfur mobilization.

They are significant because they challenge the idea that eukaryotes need mitochondria to be classified as eukaryotic. However, they have other membrane-bound organelles such as a nucleus and Golgi apparatus, meaning they remain eukaryotic.

Research suggest they lost their mitochondria over time, rather than never having had them throughout their ancestry.

Because of all these reasons, they still meet the definition of a eukaryote.