This paper presents a novel non-coherent chaotic communication system (CCS) based on machine learning (ML) approach with feature set, which includes quantified return map analysis (QRMA) metrics. In the study, so-called distance RMA (dRMA) metric has been employed for chaotic signals estimation at the receiver side, along with several other common signal characterization metrics. The obtained features vector was used to recognize binary symbols encoded in chaotic wave produced by the transmitter using parameter modulation technique. The performance of the proposed system is evaluated under different noise conditions and compared with coherent chaotic communication system. We comparatively show that the non-coherent approach improves noise resistance up to 10 dB maintaining the same bit error rate (BER). These findings suggest that the non-coherent system with dRMA metric in ML-based detector is a robust solution for secure chaos-based communication in high-noise environments.