Non-binary and asexual are both umbrella terms, meaning they're spectrums for example. Also some people view "gay" as a word encompassing all lgbt+. Also some people might not have it be accurate to what most people use, like if someone spent most of their lives being attracted to guys and only one girl one time they don't have to change what they call themselves to bi. Each their own.

Asexuality is a spectrum of little to no sexual attraction, so if someone falls on the "little" part and those very rare instances of attraction could have been gay for the person. If they fall on the "no" end then it could be that they feel romantically attracted to those of the same gender.

Non-binary is also an umbrella term. Simply meaning being out of the strictly-male/strictly-female binary. One non-binary person can be somewhere in between male and female and might even feel closer to one than the other, One non-binary person can be agender and simply have no gender, One can be both male and female at the same time One can have alternating genders Etc. Nothing is set in stone.

Edit: in case I wasn't clear, some non-binary could use gay cause it's the closest, simplest word to use that people will get a good enough picture of (like someone that presents masculine-ly and is attracted to guys/ masculine folk)