The Maxwell construction together with molecular dynamics simulation is used to study the gas-liquid phase coexistence of quasi-two-dimensional Stockmayer fluids. The phase coexistence curves and corresponding critical points under different dipole strength are obtained, and the critical properties are calculated. We investigate the dependence of the critical point and critical properties on the dipole strength. When the dipole strength is increased, the abrupt disappearance of the gas-liquid phase coexistence in quasi-two-dimensional Stockmayer fluids is not found. However, if the dipole strength is large enough, it does lead to the formation of very long reversible chains which makes the relaxation of the system very slow and the observation of phase coexistence rather difficult or even impossible.