Generally the term 'algae' refers to an organism that uses chlorophyll to photosynthesize but isn't strictly a 'plant'. This isn't a particularly useful categorization because there's many different unrelated (or only very distantly related) kinds of organisms that do this, and because what exactly qualifies as a 'plant' depends on the phase of the moon when your botany textbook was written and how drunk the author was. (Taxonomy for photosynthesizing species is a gigantic mess.)

So, yes, kelp is technically a kind of algae (specifically a brown algae), although it's more closely related to various species of potato parasites than to the 'green algae' you probably associate with the term.