These other commenters are just saying "it's algae" but the thing about that is that taxonomy is a fuck: brown algae such as kelp are classified in kingdom Chromista, so they are not plants by any taxonomic definition; however green and red algae such as nori^[Nori as I understand it is a culinary term usually referring to red algae but sometimes referring to green algae.] are on the other hand both in Archaeplastida, or kingdom Plantae sensu lato. Green algae are more specifically in Viridiplantae, or kingdom Plantae sensu stricto — but neither green nor red algae are in Embryophyta, which is kingdom Plantae sensu strictissimo.

So basically, depending on how you define plant, either some seaweed is plants, or no seaweed is plants. At least as far as I understand it.