The tradition of debate in India that this article is about (or dialogue, or dialectic, or whatever you want to call it) is very interesting, and unfortunately not well-known because most of the sources on the topic quickly get into technicalities.

Two non-technical (somewhat accessible to the general public) sources I've found are:

1. The book “Religions, Reasons, and Gods” by the late John Clayton has many interesting essays that touch on the vāda tradition. One of his interesting points is that the goal of dialogue need not be consensus or establishing common ground, but simply the “clarification of defensible difference”: understanding the other party better, and coming to shared understanding of what our differences are. Some of it is also touched on in his lecture here: http://www.bu.edu/religion/mar25-98/

2. Elaborating on the jalpa/vitaṇḍa mentioned in this article, the nyāya tradition recognized a long list of logical fallacies and poor arguments that were grounds for losing a (formal) debate. A list I've found is in the paper “Twenty-Two Ways to Lose a Debate” (https://doi.org/10.1007/s10781-009-9083-y) which also carries out some comparison with the ideas of Grice.