The bait is strong in this one.

Dragoon was used (in old games as far as i know) cause of the character limits, you can imagine in japanese they don't have to worry about them as much. And then it just stuck.

Also lorewise in FF2 and FF4 they were mounted as far as i know.

In XIV you could also argue that dragon knight would be somewhat heretic cause the Ishgardians hated (and some still do) dragons, so why naming your knights directly after the enemy? So Dragoon would be the compromise between an accurate job description and staying away as far from the hated word dragon as possible. Since dragoons are basically a counter measure against the obviously flying dragons as we see in the HW trailer and the story.