The rapid deployment of mega-constellations is driving the long-term vision of space data centers (SDCs), where interconnected satellites form in-orbit distributed computing and learning infrastructures. Enabling distributed federated learning in such systems is challenging because iterative training requires frequent aggregation over inter-satellite links that are bandwidth- and energy-constrained, and the link conditions can be highly dynamic. In this work, we exploit over-the-air computation (AirComp) as an in-network aggregation primitive. However, conventional coherent AirComp relies on stringent phase alignment, which is difficult to maintain in space environments due to satellite jitter and Doppler effects. To overcome this limitation, we propose OptiVote, a robust and communication-efficient non-coherent free-space optical (FSO) AirComp framework for federated learning toward Space Data Centers. OptiVote integrates sign stochastic gradient descent (signSGD) with a majority-vote (MV) aggregation principle and pulse-position modulation (PPM), where each satellite conveys local gradient signs by activating orthogonal PPM time slots. The aggregation node performs MV detection via non-coherent energy accumulation, transforming phase-sensitive field superposition into phase-agnostic optical intensity combining, thereby eliminating the need for precise phase synchronization and improving resilience under dynamic impairments. To mitigate aggregation bias induced by heterogeneous FSO channels, we further develop an importance-aware, channel state information (CSI)-free dynamic power control scheme that balances received energies without additional signaling. We provide theoretical analysis by characterizing the aggregate error probability under statistical FSO channels and establishing convergence guarantees for non-convex objectives.