The visible range corresponds to the typical energy differences between different states of an outer electron in a molecule, which also correspond to the typical energy differences between the input and output molecules of a chemical reaction.

(The near infrared range corresponds to the typical energy differences between different vibrational states of the atoms in a molecule. Such energy differences are smaller than the energy differences encountered in most chemical reactions, which involve extracting or adding atoms from/to the molecule, which obviously needs more energy than the vibration of those atoms, when they remain bound in the molecule.)

Thus it is normal and expected that the output molecules of an exothermic chemical reaction may be in an excited state from which they can decay to their ground state by emitting light exactly in the visible range.

As long as it is living, in any organism a lot of exothermic chemical reactions happen. In many cases the energy produced by those reactions is used for something useful for the organism (i.e. the excited output molecules transfer their surplus energy to other molecules), but it also may escape as emitted light, reducing the efficiency in the use of the energy produced by an exothermic chemical reaction to less than 100% (the efficiency is also reduced when the energy of the excited molecule is transferred to other molecules than those intended, which eventually results in warming the environment instead of doing useful work).