The "fire" is largely a heat problem. The battery is typically already short-circuited internally, which causes it to heat up. This results in boiling and vaporizing internal electrolyte, which catches fire in air. Dunking it in water primarily cools the battery to stop this process. It also short-circuits it to some extent, but the water absorbs the energy of that short circuit effectively.

Lithium-ion batteries contain a lot of energy for their size, but it's nothing like the energy available from household power circuits, which as you say, don't mix well with water.