This sentence doesn't make any sense. Not in English, at least.
I think"I do not have any party" is good English. Will Rogers said, "I belong to no organized political party; I'm a Democrat."
It certainly is not good English! I have no idea what it means and I am English!
Surely the meaning of 'partido' in this context is game or match, isn't it?
No, it means "I'm not part of a political party". Except when they say "tomar partido", which means to take side.
Even knowing what it means, it still feels like an awkward translation. "I don't have a party" seems better.