Does someone have an explanation for this?

Pretty simple comparrason, it's like how a water cooler in a computer works, it takes the heat away through conductivity.

Water stops fire

Have you heard this artist yet?

Pretty obvious. The water keeps the temperature of the inside of the cup below the flash point of the cardboard.

Old trick. Used to use it as a bet. Boil water in the cup before burning the cup. The water acts as a heat transfer through the cardboard. Pulls the heat away.

surface tension?

Combustion energy has been utilised for water's vaporization.

The lindenfrost efect

@WhoHadOneJob Yes, water.

Boiling is a cooling process. The latent heat of vaporization. Condensation is a heating process. So when a glass with a cold drink sweats, it's gaining heat.

the water absorbs the heat