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

The mitochondrion is a normal organelle essential for the eukaryotic cell, this defines a eukaryotic cell.

Mitochondria is the place of cellular respiration which is reactions that convert glucose into ATP, an energy molecule.

However, there are still exceptions to the rule, as is the case for this eukaryotic cell Monocercomonoides sp. which is an anaerobic protozoa, devoid of mitochondria, and therefore lives without cellular respiration. it would have an alternative system of sulfur mobilization, fulfilling the same functions as the mitochondria.