CERN-LHC. A search for exclusive or quasi-exclusive gamma gamma to W+W- production, via pp to p(*) W+W- p(*) to p(*) mu+/- e-/+ at sqrt(s) = 8 TeV, is reported using data corresponding to an integrated luminosity of 19.7 inverse femtobarns. Events are selected by requiring the presence of an electron-muon pair with large transverse momentum pt(mu+/- e-/+) > 30 GeV, and no associated charged particles detected from the same vertex. The 8 TeV results are combined with the previous 7 TeV results (obtained for 5.05 inverse femtobarns of data). In the signal region, 13 (2) events are observed over an expected background of 3.9 +/- 0.6 (0.84 +/-0.15) events for 8 (7) TeV, resulting in a combined excess of 3.4 standard deviations over the background-only hypothesis. The observed yields and kinematic distributions are compatible with the standard model prediction for exclusive and quasi-exclusive gamma gamma to W+W- production. Upper limits on the anomalous quartic gauge coupling operators a[W;0,C] (dimension-6) and f[M0,1,2,3] (dimension-8), the most stringent to date, are derived from the measured dilepton transverse momentum spectrum.