The current evaluation of Large Language Models (LLMs) predominantly relies on benchmarks focusing on their embedded knowledge by testing through multiple-choice questions (MCQs), a format inherently suited for automated evaluation. Our study extends this evaluation to explore LLMs' pragmatic competence--a facet previously underexamined before the advent of sophisticated LLMs, specifically in the context of Korean. We employ two distinct evaluation setups: the conventional MCQ format, adapted for automatic evaluation, and Open-Ended Questions (OEQs), assessed by human experts, to examine LLMs' narrative response capabilities without predefined options. Our findings reveal that GPT-4 excels, scoring 81.11 and 85.69 in the MCQ and OEQ setups, respectively, with HyperCLOVA X, an LLM optimized for Korean, closely following, especially in the OEQ setup, demonstrating a score of 81.56 with a marginal difference of 4.13 points compared to GPT-4. Furthermore, while few-shot learning strategies generally enhance LLM performance, Chain-of-Thought (CoT) prompting introduces a bias toward literal interpretations, hindering accurate pragmatic inference. Considering the growing expectation for LLMs to understand and produce language that aligns with human communicative norms, our findings emphasize the importance for advancing LLMs' abilities to grasp and convey sophisticated meanings beyond mere literal interpretations.