Perhaps it's been changed since you posted this link but I see nothing about microalgae being plants.

From the article: "Unlike higher plants, microalgae do not have roots, stems, or leaves."

"Higher" here to me implies microalgae are also plants, otherwise the qualifier isn't needed.

The article for "algae" says: "No definition of algae is generally accepted. One definition is that algae 'have chlorophyll as their primary photosynthetic pigment and lack a sterile covering of cells around their reproductive cells'. Some authors exclude all prokaryotes thus do not consider cyanobacteria (blue-green algae) as algae."

So it seems a little silly to me to split hairs about whether algae are plants in an popular audience news article about a food product.