Kakashi said that Hyuga have the power to enhance their chakra flow which is what Gates is.
Gai's taijutsu involves the control of chakra network and as we know that is the Hyuga's signature power. Ashura was the first SM user and humans most likely learned how to control NE from him. It's likely that taijutsu users learned how to use Gates from Hamura because he would be the only one with the knowledge of how the chakra network functions.
In addition, Naruto proved that Six Path Senjutsu can negate the side effects of 8 Gates, Hamura was a taijutsu god with Six Path Senjutsu, if anything Gates would be his way of rivalling JJ Hagoromo's power since Yin = Yang. There's nothing to suggest he wasn't able to use Gai's taijutsu.
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Gai's taijutsu involves the control of chakra network and as we know that is the Hyuga's signature power. Ashura was the first SM user and humans most likely learned how to control NE from him. It's likely that taijutsu users learned how to use Gates from Hamura because he would be the only one with the knowledge of how the chakra network functions.
In addition, Naruto proved that Six Path Senjutsu can negate the side effects of 8 Gates, Hamura was a taijutsu god with Six Path Senjutsu, if anything Gates would be his way of rivalling JJ Hagoromo's power since Yin = Yang. There's nothing to suggest he wasn't able to use Gai's taijutsu.