Equipment: Intense candle for nabemono. What is it?
Sounds like they were using タブレット型固形燃料 taburetto-gata kokeinenryou, literally "tablet-shaped solid fuel":



(courtesy メシ通)

The market leader is a company called Nitinen, who offer a wide range of different sizes and shapes.  The primary ingredients are methanol and alcohol, blended with fat in much the same way as soap.