Some enby people consider themselves trans and some don't.
The enbys who consider themselves as transgender typically see gender in two different categories. For them there is cis (identifying as boy/girl with a matching male/female sex) and everything else is transgender. In a way, there is at least a social transition for anyone with identities beyond cis so there's a valid argument to be made there.
For me personally, I am part of the group that doesn't view themselves as transgender. I roughly view gender in the categories of cis, demigender, agender, nonbinary, mutltigender, genderfluid, and transgender. While its possible for someone to be in multiple of these groups at the same time (such as myself), I feel like it's the best way for me to understand and organize gender. The reason I choose to have more categories than just Cis and trans is because people with these identities that I listed have a different experience of gender than one another. A person who has multiple genders is going to have quite a different experience than someone who doesn't feel strongly connected to gender at all, and so on. Because of this, I personally don't think they should be shoved into the same category group.
There isn't a standard on how to view gender in terms of categories beyond some umbrella terms though. Gender is a very personal experience. So at the end of the day, it's up to you if you consider yourself as transgender or not May and neither answer is wrong.