Chess, a deterministic game with perfect information, has long served as a benchmark for studying strategic decision-making and artificial intelligence. Traditional chess engines or tools for analysis primarily focus on calculating optimal moves, often neglecting the variability inherent in human chess playing, particularly across different skill levels. To overcome this limitation, we propose a novel and computationally efficient move prediction framework that approaches chess move prediction as a behavioral analysis task. The framework employs n-gram language models to capture move patterns characteristic of specific player skill levels. By dividing players into seven distinct skill groups, from novice to expert, we trained separate models using data from the open-source chess platform Lichess. The framework dynamically selects the most suitable model for prediction tasks and generates player moves based on preceding sequences. Evaluation on real-world game data demonstrates that the model selector module within the framework can classify skill levels with an accuracy of up to 31.7\% when utilizing early game information (16 half-moves). The move prediction framework also shows substantial accuracy improvements, with our Selector Assisted Accuracy being up to 39.1\% more accurate than our benchmark accuracy. The computational efficiency of the framework further enhances its suitability for real-time chess analysis.