Yes, so the participants in the debates were doing it for what if not to prove their religions? And the audience was their either to bee converted or to enjoy themselves.

The Mongols held theological debates, for various reasons. It was a novel thing in that place at the time. Political reasons, cultural reasons, and pure curiosity from Genghis and subsequent leaders. The Mughal (term derived from mongol, although they had a tenuous relationship) leader Akbar did similar things about 300 years later.

I recommend reading Genghis Khan and the Quest for God if you want further information.

https://www.amazon.com/Genghis-Khan-Quest-God-Conqueror/dp/0...