DragonRaiderX9: For clarity, I did a full shutdown, then restarted. Apparently just restarting won't work, at least according to the Steam forums. I suppose I should still try it, but I can't imagine it would change much.
It depends, for example Windows 10 tries to load itself faster by hibernating some of its processes on normal shutdown, so unless one was holding the Shift key while selecting Shutdown or running the "shutdown /s /f /t 0" command as an admin from the command line, they may have to shutdown again with either of those ways or reboot to be sure that every process is restarted properly.
And of course you never mentioned what GPU you have and what driver version for it you have installed, while the graphics requirements for Ys 1 seem to low enough that almost any GPU you can fit into a computer with an i5 CPU should be able to not meet them, there might be a known problem with your current drivers that is causing the DirectX error and installing a more recent or older driver could fix that.