Unlike the Latin script, Khmer does not use spaces between words, leading to text recognition typically being done at the textline level. This results in high latency for a language-aware autoregressive (AR) decoder that decodes one character at a time by conditioning on previously-decoded characters. On the other hand, a non-autoregressive (NAR) decoder decodes characters in parallel by assuming no character dependencies; hence, it is not language-aware. For the same feature extractor, an AR decoder not only achieves higher recognition accuracy but also incurs higher latency compared to an NAR decoder. In this paper, we introduce an efficient Khmer textline recognition method based on an NAR decoder, ensuring low decoding latency while maintaining character dependencies and, consequently, linguistic awareness. This is achieved by utilizing a Khmer-specific subword modeling approach that captures the syntactic, morphological, and orthographic aspects of the Khmer script. Instead of character-level recognition, the proposed method recognizes Khmer subwords (i.e., character clusters) in parallel and, thus, character dependencies are implicitly captured. The experimental results demonstrate that the proposed method outperforms the character-level baseline NAR model in terms of recognition accuracy while maintaining the same low latency. When compared with the character-level baseline AR model, the proposed method achieves comparable or improved recognition accuracy while also achieving significantly lower latency. When compared with the recent state-of-the-art (SOTA) NAR and AR Khmer textline recognition methods, our proposed method achieves superior recognition performance.