I find that it actually switches priorities depending on if it is the active application or not. If it's the active program it will switch to normal priority, likewise if it's the background application [not the one in focus] it switches to low priority instead. Since you're seeing it as low in the task manager, FFXIV has already switched to low as it was then not the active application up front.

One can monitor the priority changes themselves as they wish by using a few batch commands in a loop outside the program to log program priority settings.