PtSe_{2} is a van der Waals material transitioning from an indirect band gap semiconductor to a semimetal with increasing thickness. Its absorption threshold has been conjectured to originate from interband indirect transitions. By quantitative comparison between broadband (0.8-3.0 eV) optical absorption of high-quality exfoliated crystals and DFT ab initio simulations, we prove instead that the optical absorption arises only from direct transitions. This understanding allows us to shed light on the semiconductor-to-semimetal transition in an emblematic strongly thickness-dependent 2D material, and to explore the effect of stacking and excitons on the optical absorption.