What bacteria shed harvestable energy from root zone organic matter?
Short answer
It is known that a great variety of soil micro-organisms is able to use solid anodes as electron acceptor for their metabolism, thus creating some electrical current. Geobacter spp., Clostridia and Deltaproteobacteria are among them (1). However, I could not find any extensive list of these microbes. It is likely that a large number of these microbes is not identified yet.
A review on Plant Microbial Fuel Cells was recently published and might interest you (2).
Long answer
Plant Microbial Fuel Cells are a special case of Microbial Fuel Cells
The system presented at your first figure is being developed by the Dutch company named Plant-e and falls within the concept of Plant Microbial Fuel Cells (PMFC).
Simply put, a Microbial Fuel Cell (MFC) is a device in which chemical energy contained in chemical bounds of organic substrates is converted to electrical energy by microbes. Microbes consume the organic substrates while using the anode as the final electron acceptor of their metabolism. Microbes capable of using anodes as electron sinks for their metabolism are called electrogens.
PMFCs are a special case of MFCs, taking advantage of the microbe/plant interactions. Organic substrate is supplied to microbes directly by the plant and you get two benefits: plant biomass and electricity production.
Complex interactions between plant and microbial communities
As you noted in your last sentence, no particular species of plant was cited. Indeed various PMFCs strategies were implemented, based on various species of plants, such as Glyceria maxima, or Oryza sativa (rice) (2). The plant species is not the only key factor for efficient PMFCs: the nature of the organic substrates provided by plants to microbes, the soil's characteristics, the electrodes' characteristics, and the nature of the inoculum are crucial factors too.
Regarding the microbiological aspect, it appears that pure culture (single species) PMFCs are not necessarily the best alternative. Plants provide microbes with a variety of chemical compounds, which may not be all consumed by a single species. Only a well adapted microbial community is likely to be able to take advantage of all these compounds and to include efficient electrogens. The path from plant products to electrical current is more likely to be a complex microbial food web, rather than a single species' metabolism. In practice, most studies seem to rely as soil as the incolum (2).
So, concerning your initial question: we might not have identified yet every soil electrogens. Several are, however, already well known, such as Geobacter sulfurreducens. But, what is important is that most (P)MFCs strategies rely on microbial communities as a whole, in a 'black box' way.

References
(1) Dunaj, S.J. et al. Relationships between Soil Organic Matter, Nutrients, Bacterial Community Structure, And the Performance of Microbial Fuel Cells, Environment Science and Technology, 2012, 46 (3), pp 1914-1922
(2) Nitisovarut, R., Regmi, R., Plant microbial fuel cells: A promising biosystems engineering, Renewable and Sustainable Energy Review, 2017, 76, pp 81-89