according to my research zoochlorella is an green algae.
A lot of sea anemones have a facultative ectosymbiotic relationship with zooxanthellae and/or zoochlorella. Obviously these need light to carry out photosynthesis, and so in that sense yes, they do need light. However it is not really the anemone that needs the light, it's the algae and the anemone can survive without the algae, so in that sense no, they don't need light. It depends on what you meant by the question.
Algae thrive in warm temperatures (around 75-85°F) with plenty of sunlight and nutrients available. They also require still or slow-moving water with a slightly basic pH level for optimal growth. Too much heat or cold, excessive sunlight, or imbalanced nutrients can inhibit algae growth.