With the rapid development of autonomous driving and extended reality, efficient transmission of point clouds (PCs) has become increasingly important. In this context, we propose a novel channel-adaptive cross-modal generative semantic communication (SemCom) for PC transmission, called GenSeC-PC. GenSeC-PC employs a semantic encoder that fuses images and point clouds, where images serve as non-transmitted side information. Meanwhile, the decoder is built upon the backbone of PointDif. Such a cross-modal design not only ensures high compression efficiency but also delivers superior reconstruction performance compared to PointDif. Moreover, to ensure robust transmission and reduce system complexity, we design a streamlined and asymmetric channel-adaptive joint semantic-channel coding architecture, where only the encoder needs the feedback of average signal-to-noise ratio (SNR) and available bandwidth. In addition, rectified denoising diffusion implicit models is employed to accelerate the decoding process to the millisecond level, enabling real-time PC communication. Unlike existing methods, GenSeC-PC leverages generative priors to ensure reliable reconstruction even from noisy or incomplete source PCs. More importantly, it supports fully analog transmission, improving compression efficiency by eliminating the need for error-free side information transmission common in prior SemCom approaches. Simulation results confirm the effectiveness of cross-modal semantic extraction and dual-metric guided fine-tuning, highlighting the framework's robustness across diverse conditions, including low SNR, bandwidth limitations, varying numbers of 2D images, and previously unseen objects.