This study utilizes the game Codenames as a benchmarking tool to evaluate large language models (LLMs) with respect to specific linguistic and cognitive skills. LLMs play each side of the game, where one side generates a clue word covering several target words and the other guesses those target words. We designed various experiments by controlling the choice of words (abstract vs. concrete words, ambiguous vs. monosemic) or the opponent (programmed to be faster or slower in revealing words). Recent commercial and open-weight models were compared side-by-side to find out factors affecting their performance. The evaluation reveals details about their strategies, challenging cases, and limitations of LLMs.