SNK created the game and developed the original Neo Geo version and thus own the rights to Fatal Fury; any port, including this one, must have their name on it. However, they did not develop the home ports. MobyGames is very unreliable for developer information; they often just take one port's developer for all the ports and need correction in general (sometimes even getting publishers wrong). If you check the staff list on MobyGames for this X68000 port you'll find that many of the people who worked on it were employees of Home Data/Magical Company, as they worked on other products by that company, and this is the same conclusion the much more reliable
GDRI came to.
The publisher can be inferred
from the box. Note the use of stickers, as the game was released right after the company changed their name.