Radio maps enable intelligent wireless applications by capturing the spatial distribution of channel characteristics. However, conventional construction methods demand extensive location-labeled data, which are costly and impractical in many real-world scenarios. This paper presents a blind radio map construction framework that infers user trajectories from indoor multiple-input multiple-output (MIMO)-Orthogonal Frequency-Division Multiplexing (OFDM) channel measurements without relying on location labels. It first proves that channel state information (CSI) under non-line-of-sight (NLOS) exhibits spatial continuity under a quasi-specular environmental model, allowing the derivation of a CSI-distance metric that is proportional to the corresponding physical distance. For rectilinear trajectories in Poisson-distributed access point (AP) deployments, it is shown that the Cramer-Rao Lower Bound (CRLB) of localization error vanishes asymptotically, even under poor angular resolution. Building on these theoretical results, a spatially regularized Bayesian inference framework is developed that jointly estimates channel features, distinguishes line-of-sight (LOS)/NLOS conditions and recovers user trajectories. Experiments on a ray-tracing dataset demonstrate an average localization error of 0.68 m and a beam map reconstruction error of 3.3%, validating the effectiveness of the proposed blind mapping method.