Algae and greenhouse effect
In most situations the lack of sufficient CO2 is not what is limiting algal growth. In general the limits to growth are set by the availability of nutrients such as iron, nitrogen and silica. They actually touch on that in the paper. For example removing iron limitation has a much more dramatic impact on algal growth or blooms than increasing CO2 by a few percentage points (see here). This also explains why there are more algal blooms, the increase of fertilizer use results in more food for the algae to grow on and all round bad things (see here). 

Perhaps some algae will benefit since they will not have to invest much energy/nitrogen in creating carbon concentrating mechanisms. However several species of algae use calcium for their cell walls and these would actually suffer by increased CO2 concentrations as this leads to ocean acidification (e.g. coccolithophores). Taking into account that these are heavy sinking algae that take a lot of carbon with them to the ocean floor and you see that ocean acidification is not likely to be a good thing.