For what is reaction enthalpy more relevant than reaction free energy?
While a detailed answer to this question could go on at length, the major practical distinction is the following:


The enthalpy change of a reaction/process indicates how much heat input or output is involved with the reaction, with a negative $\Delta H_\mathrm{rxn}$ indicating heat output.
As you note, the Gibbs free energy change of a reaction/process indicates whether a reaction is thermodynamically favored or disfavored, with a negative $\Delta G_\mathrm{rxn}$ indicating a favorable reaction.


Note that, e.g., a reaction/process can have $\Delta H_\mathrm{rxn} &gt; 0$ (endothermic), but also $\Delta G_\mathrm{rxn} &lt; 0$ (thermodynamically favored).  That is, despite the reaction requiring heat input, it is still favored to occur.  This is because the change in entropy of the process, $\Delta S_\mathrm{rxn}$, is sufficiently large that the $T\Delta S_\mathrm{rxn}$ term is able to overcome the positive $\Delta H_\mathrm{rxn}$.  A common example is the endothermic dissolution of various salts, such as ammonium nitrate $\left(\ce{NH4NO3}\right)$.

Thus, the paper probably used the enthalpy results because they were comparing their calculations to experimentally-measured enthalpies (heats) of their process(es) of interest.