LLMs like GPT4 operate on tokens, not characters, so they're operating with a severe handicap when playing those sorts of games -- they see a word like "robot" as a single token, not as a collection of letters, so they don't know that it starts with the letter R unless that fact appeared in its training material.

Interestingly, they do better at rhyming games, because those are based on associations between tokens which are easier to infer from usage in poetry, or by reading rhyming dictionaries.