While it is certainly true that peerScholar provides a logistically reasonable way of having critical thinking and writing assignments in any size classroom, its primary benefits are pedagogical. That is, peerScholar is transformative in the sense that it reflects an educational enhancement over the standard approach of having an expert do the grading. Specifically...
In a typical assignment context the only "answer" that students see to an open-ended written assignment is their own answer. It is difficult to truly know how strong one's ideas and communication are when they never get a chance to directly compare them to the ideas and communication of others. Thus, by seeing the work of peers, some of which might be worse and some better than their own, students are given a very strong sense of their own skill levels.
It is sometimes said that teachers cannot make students learn, they can only make them want to learn. The process of learning is controlled by the student, and all the teacher can really do is motivate, and provide contexts that will provoke learning. When students are shown six examples of their peers work and are asked to discriminate among them based on quality, the student is suddenly put in the role of deciding what is and is not good, and why. They are provided a rubric as a guide, but ultimately the student "knows" that certain pieces are stronger than others, but must then "figure out" what makes certain pieces strong or weak. This sort of active perspective on learning is much more powerful than someone else simply listing the features of a well written piece. That is, it supports a deeper form of learning. See the research on peerScholar link for evidence of this efficacy.
As highlighted in the description, thanks to the automated nature of the peerScholar system, assignments can be performed in a condensed time period. Thus, students receive feedback on their work not long after composing it, and most definitely while it is still fresh. Moreover, given their own experiences as marker, they are in a much stronger and more informed position when assessing the feedback given to their own work. Thus the feedback is timely and rich, and this all supports strong learning.
Note also that while peerScholar has been primarily used to support written assignments as discussed, it's potential for use is broad. As one example, a photography professor might ask her students to take pictures that emphasize light and shadow, with each student submitting their best picture on Monday by midnight. Students could then assess the pictures submitted by their peers according to a rubric and also based on their own learning as they compare the pictures and grade them. All of the same learning and logistic advantages would be there in this very different domain. As long as the target is something that can be presented digitally, and the "answer" could be submitted digitally, the system would support it. Thus, while it is described primarily as a tool to support critical thinking and clear written communication, it is more generally an innovation that supports deep learning via peer-assessment.