Here are some ideas that I'd like to discuss. I don't believe in historicity as some kind of fetish. Every bunkai that works is valid bunkai. Speculating and comparing is fun though, and could lead to different perspectives and new (or old) bunkai.
The second form "24 steps" (二十四步) in this video displays some striking similarities to Naihanchi - the sideways action, cross stepping, stomping and some of the hand patterns. 二十四步 is pronounced Nijushiho in Japanese. The colloquial Hokkien pronunciation used to be nn̄g-cha̍p-sì with a rasping h sound. Sounds a little something like Naihanchi to me. The video's description hints at a connection to Five Ancestors Fist, which in turn influenced Karate.
I find some degree of connection plausible.
Roots of Shotokan by Joe Swift sums up what people have written about Naihanchi's/Tekki's origin.