What you describe is not a contrast to chess. Current LLMs also do not play chess well. Generally they play at the 1000-1300 ELO level. Playing specific games

What you describe is not a contrast to chess. Current LLMs also do not play chess well. Generally they play at the 1000-1300 ELO level. Playing specific games well requires specialized game-specific skills. A general purpose LLM generally lacks those. Future LLMs may be slightly better. But for the foreseeable future, the real increase of playing strength is having an LLM that knows when to call out to external tools, such as a specialized game engine. Which means that you're basically playing that game engine. But if you allow an LLM to do that, there already are poker bots that can play at a professional level.