Nah, it’s more of a follow up joke. The first joke is just putting Chai into ChatGPT, which is already funny and clever. Then the follow up jokes where they put appropriate words for the GPT and AI acronyms.
"Chai" doesn't mean "tea" in English though - it signifies a specific type of mixed-spice tea. "Chai tea" is no more redundant in English than "Earl Grey tea" is.
One a word has been borrowed into another language, the meaning/etymology of the word in the source language is irrelevant. For example, I bet when you say "sushi" you mean "fish on/wrapped in rice" and not the vinegared rice itself, because that's what it means in English. Similarly, when a Japanese speaker says "mansion", they mean a high-rise apartment or condominium, not a large house, because that's what the word means in Japanese.