I...honestly don't hear any connection between the two pieces linked by the OP. And the complete "Four Fiends" theme is already remixed and used in the game during EW (Barbariccia fight). I really can't fathom any connection between the Arcadion and the Four Fiends from FF1.

In fact it is probably more likely they won't be directly referenced by name but by thematics and design.
This I could see happening, but not really in any way because of the Four Fiends, just rather naturally including the four main elements that get included a lot throughout the game. We already have the four remaining parts of Living Memory dedicated to Earth, Wind, Fire, and Water. It's just a common theme.