There is a lot of the word "seaweed" repeated in the article, but they are talking about brown macroalgae. A group comprising a few families inside the huge diversity of extant algae.
Pointing this can seem pedantic, but the detail is important. Brown macroalgae evolved to live in cold waters. In the limit of their distribution you raise the minimum water temperature two degrees and the plant is unable to reproduce anymore. As they have short lives, at 25 celsius degrees they went locally extinct very fast. Is their kryptonite.
Moreover, they are adapted to live in a permanent state of guerrilla quiting warm areas on years with "The Niño" event, and massively recolonizing the area in the next year. This is the reason for their famous superfast growth.
In extensive areas of the south of Europe, entire submarine forests of the "european Kelp" Laminaria and Saccorhiza (comprising a huge biomass) went in an accelerate decay and are totally gone in the last few decades. They can't return because the local average temperature raised a few degrees in the coastal areas. We need to keep this in mind if we count in this creatures to store our excess of carbon.