Why is there a (G) in the chemical equation of water gas? What does this mean? Why don't you shoot an arrow?

This (g) refers to gas, because this reaction is carried out at high temperature and high pressure, and C reacts with water vapor, so the state of water should be indicated.

Arrows are not written because there is gas in the reactant (water vapor in this reaction), so the gas in the product can be written without arrows, for example, C+O2=CO2, and similar reactions will not write arrows.