This is a semantic argument. The outcome depends on how you define "living".
Any definition that includes fire (i.e. hot air) is so broad that it makes the word "living" meaningless and useless. If you included fire, you'd perhaps have to include water or any other fluid.
The argument cannot be made for water as it does not respire or digest.
Yes, the definition of life that fire fits in is broad. But it is still the definition of life.
I don't know how you define "respire", but water dissolves and releases gases. Fire is a gas, so it can't "respire" the same way. It is just one gas or another.
As for digestion, water is a powerful solvent that breaks many things down. Fire just heats them up, which may or may not change their chemical structure.
Living organisms are a subset of fire—controlled exothermic processes. But when your exothermic process becomes uncontrollable, your life-force is used up quickly.
I don’t see how to define organism without cells.