An analysis of hadron production by two-photon interactions has been performed using data taken with the PLUTO detector at the e+e- storage ring PETRA. The data sample comprises 1243 events with invariant mass between 4 and 13 GeV, where one of the scattered beam electrons is detected in a tagging shower counter. This sample corresponds to an integrated lumionosity of ~40 pb-1 at a beam energy of 17.3-17.5 GeV. Using these events, a search has been made for evidence for a pointlike coupling of photons to quarks. The theoretical properties of such an interaction are discussed: it is concluded that a signature of the process is the production of hadron jets at high transverse momentum relative to the virtual photon direction.' Clear evidence for high PT jet production is found in the data, at a level consistent with the predictions of the quark parton model. The existence of the pointlike coupling is thus demonstrated. For values of the virtual photon mass squared between -1 and -18 GeV2, it is shown that the data can be completely explained by a combination of vector meson dominance and the quark parton model. A thrust analysis indicates that the entire data sample in this virtual photon mass range is consistent with the hypothesis of a two-jet final state. At smaller values of the virtual photon mass squared (-0.1 to -1.0 GeV2) it is found that the data cannot be explained by pure two-jet production. A good representation of the observed thrust and jet transverse momentum distributions is, however, obtained by requiring that a significant fraction (~20%) of the events produce an isotropic final state. The dependence of the proportion of isotropic events on the mass of the virtual photon is shown to be comparable to vector dominance. Possible interpretations of this result are discussed.