I'm not a Japanese speaker, but from what I can tell, the ban on Hanafuda was lifted before Nintendo was founded - in fact some link the lifting of the ban to founding of Nintendo as the founder enjoyed the cards and wanted to produce good quality cards.

This might come from not being a Japanese speaker, but I'd also wonder how "Nintendo" translates to a sentence including "hanafuda" without any of the syllables referring to hanafuda (except perhaps the "do")