By "serious" I mean: The premise is not a scam
It doesn't seem to be a scam, in that it is supported by Wageningen University & Research -- one of the most prestigious academic institutions in the Netherlands, and possibly the most prestigious agronomy institute in the world.
Having said that, a number of the claims in the press release that you linked are exaggerated or excessively optimistic. Notably, this research was originally academically published in 2007, then publicised in 2012 with the claim that there would be a product on the market within a year, with "larger-scale electricity production in marshlands around the world following after 2015." That hasn't happened. As of October 2018, their only products are barely more than toys, producing tiny amounts of power; just enough to drive decorative lamps. (Probably a few milliwatts.) Further, they can only operate when carefully tended: their FAQ still says:
Plant-e is currently developing a system that can be applied in existing, wet nature areas such as ...
So some eleven years after developing the process, and six years after claiming a product release was imminent, they do not yet have a system that works in a natural environment.
It works by taking advantage of the up to 70 percent of organic material produced via photosynthesis that can’t be used by the plant and is excreted through the roots.
This paragraph is troubling, although it may not be their fault -- academic press releases often get garbled by publicists. The only organic material produced from (plant based) photosynthesis is sugar; all other processes either build up from the sugars (to make complex carbohydrates such as cellulose) or break them down (to drive other, endothermic biochemical processes.) What fraction of the sugar produced in a plant can it use? All of it; and any plant that didn't scrimp every last benefit from it would be very poorly adapted.
It is well known that the efficiency of photosynthesis is far below the theoretical optimum. Under ideal conditions is can be as high as 8%, but 4% is more typical, and in adverse conditions it can be well under 1%. However, that refers to the efficiency with which the available light energy is converted to chemical energy (in the form of sugar.) What is being said here is that after ~4% of the available light energy has been stored as sugar 70% of that hard-won sugar then leaks out through the roots and is lost. Umm, no. That doesn't happen. Not unless the plant is badly diseased, anyway.
I don't understand what they were trying to say here, and can't find a source for this 70% loss figure; but as written, it is nonsense.
As naturally occurring bacteria around the roots break down this organic residue, electrons are released as a waste product.
OK, apart from describing electrons as a waste product which is more garbling, this part is fine. Soil bacteria do indeed break down organic materials released by other lifeforms, including both plant and animal wastes, and their remains after death. And just as in higher organisms, some of these catabolic processes are electrochemical in nature, and some of this electrical energy can be diverted.
The problem is that the available power output is tiny. Which is consistent with Plant-e's reported outputs, which are about 600 times lower than a conventional solar panel.