Direct photon cross sections obtained in ppBAR and pp collisions at square-root s = 24.3 GeV at the CERN SPS, are used in a next-to-leading order QCD analysis. From the cross-section difference sigma(ppBAR --> gammaX) - sigma(pp --> gammaX), and quark distributions measured in deep inelastic scattering, a determination of the strong coupling constant, alpha(s), is performed via a measurement of LAMBDA(4)/MS . This first measurement of LAMBDA(4)/MS using direct photon data yields a value LAMBDA(4)/MS = 235 +/- 79 (stat.) +/- 70 (syst.) MeV. The corresponding value of alpha(s) expressed at M(Z)2 is alpha(s) (M(Z)2) = 0.112 +/- 0.006 (stat.) +/- 0.005 (syst.) +0.009/-0.001 (theor.). The gluon distribution in the proton for x > 0.2 is determined both from the pp and from the pp data, and the results agree with each other and with previous determinations using the same method.