We report a high-statistics measurement of the differential cross section of the process gamma gamma -> (KSKS0)-K-0 in the range 1.05 GeV <= W <= 4.00 GeV, where W is the center-of-mass energy of the colliding photons, using 972 fb(-1) of data collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider operated at and near the Upsilon-resonance region. The differential cross section is fitted by parameterized S-, D-0-, D-2-, G(0)-, and G(2)-wave amplitudes. In the D-2 wave, the f(2)(1270), a(2)(1320), and f(2)'(1525) are dominant and a resonance, the f(2)(2200), is also present. The f(0)(1710) and possibly the f(0)(2500) are seen in the S wave. The mass, total width, and product of the two-photon partial decay width and decay branching fraction to the K (K) over bar state Gamma(gamma gamma) B(K (K) over bar) are extracted for the f(2)'(1525), f(0)(1710), f(2)(2200), and f(0)(2500). The destructive interference between the f(2)(1270) and a(2)(1320) is confirmed by measuring their relative phase. The parameters of the charmonium states chi(c0) and chi(c2) are updated. Possible contributions from the chi(c0)(2P) and chi(c2)(2P) states are discussed. A new upper limit for the branching fraction of the P- and CP-violating decay channel eta(c) -> (KSKS0)-K-0 is reported. The detailed behavior of the cross section is updated and compared with QCD-based calculations.