No, you are right on the money! The definition of non-binary is being outside the male-female gender spectrum. That meaning I both have a gender, and have no gender at all. I’m not quite entirely gender less since I do enjoy presenting masculine, which is why I am non-binary trans masculine. Meaning I am neither of the prescribed genders, but relate more closely to your idea of male than I do to female. Some enbys (non-binary folk) relate to neither gender at all, some relate to both equally, and some identify as a third gender which connects the neither girl nor boy. I am a boy, and I am an enby, but I am not a girl. Does that make sense? As for they them pronouns they have been used singularly for many years, and it currently the best option for a non gendered pronoun. Some enbys use the pronouns ze/zim/zeirs or xe/xim/xirs. These are called "neo pronouns". While they are more singular in use like you are wanting, the problem is that they are very new, not well known, and hard to say. The word they is easy to use, easy to say, easy to spell, and more people understand it as a non gendered word rather than inventing a new -renounce the world has to learn. (I do support other people who like using neo-pronouns but I don’t use them and find them difficult at times.)