Wind turbines submerged in the upstream wind turbine (UWT) wake lead to reduced power production and increased fatigue loads. However, current wind farm layout optimization processes prioritize power production without addressing fatigue load due to the complexities associated with fatigue load assessment within the UWT wake. In this study, the impacts of wake-turbine overlap on the fatigue load for floating offshore wind turbines are investigated. A large-eddy simulation is used to generate the UWT wake, followed by extensive aeroelastic simulations to meticulously examine the wake-turbine overlap effect over the wake domain. The blade fatigue load results reveal significant influences on the degree of wake-turbine overlap. Blade fatigue load correlates with wake deficit and turbulence, exhibiting a bimodal distribution in the lateral direction with peaks at approximately 0.5 turbine diameter (D) offset while diminishing in the streamwise direction. Despite the complete recovery of power production at 1D lateral offset, a significant fatigue load persists. Furthermore, tower fatigue load and platform motions are notably affected by the degree of wake-turbine overlap and the wave. These findings underscore the importance of incorporating fatigue load analysis into the wind farm layout optimization process to extend the turbine lifespan and reduce operation and maintenance costs.