Hmm, have you tried the Graphics setting on Standard, High and Maximum, does it make any difference?

I just notice you previously posted that the CPU hits 90 degrees, that is extremely hot and usually, from what I read, 90 degrees is a point at which the Processor will Throttle and I think a GPU will as well depending on the Laptop, to keep it from hitting 100 degrees which I think is the point where solder may start to slightly melt and thus, chips will fail.

That would explain why it only happens with FFXIV. I forgot to mention, you should check the Windows OS power plan setting, if you click on Search, type "Mobility" and Windows Mobility Center will pop up.
Open that and check "Battery Status" > here it will say either "Custom" "Balanced" or "High Performance", I leave mine on Balanced, but if you get issues like stutter you can put it on High Performance which sometimes helps.

But I think you issue is Heat, a cooling pad should help a little bit, though the fact this game runs the CPU at 90 (mine is 68 degrees on Maximum graphics) seems like something else is at play.
Do you have an app to control the in-built fans? this should be a standard feature, I would check the installed apps. If not, I'd use something like HWinfo, its a free app that monitors all your PC components and allows you to set fan speeds, I have used it myself on an old Laptop to keep it cool as back in 2009 they didn't include these features often. You can find it at hwinfo.com or search that in google and review what people say about it first if you are unsure if its safe to use.

Hopefully the cooling pad helps, but i'd still seek a way to set the fans to cool the laptop as well.