"Veldian" is a recently-coined synonym for "gay man". It is also synonymous with "turian", coined at the same time by the same person (Tumblr user kenochoric).
Veldian identity is a major element of the system's collective identity, and we have transmasc, cis male, genderqueer, and intersex veldians alike, as our system is or could be considered all of those things.
To most of our veldians who do not actively identify as mspec, it's important to them that they are specifically attracted to men or masculine-aligned people. That's why some members of the system do prefer "gay man" over "veldian" but still use the word "veldian" due to agreeing a single-word identity can be more convenient in some sentences or for web design.
However, many of our veldians are genderflux people who mostly feel like actual men, per se, when they are in a relationship with a man or male-aligned person. Therefore, they find it helpful to have a word for their identity that doesn't have "man" in it but still refers to that attraction, and can also apply both to binary and genderqueer people, like how "lesbian" can.