Well, there's three potential reasons:

1) Playing video at the same time windowed, requires nothing, it will just work. FFXIV does have it's own frame limiter, and there is a feature to turn the frame limiter on when the game is not in focus.

2) Playing video full screen on one monitor and the game full screen on another monitor... kinda requires separate GPU's. It depends how well the game deals with the full screen switch. FFXIV on my machine for example, since it allows you to select which monitor to play on, both the iGPU or a HDMI monitor while the game is on the displayport @ 4Kp60 works. If your monitor switches to 1080i while full screen for some reason, then it will force all monitors on the same card to 30hz. This shouldn't happen, but there is a condition specific to HDMI, where if you use a 4K monitor on HDMI 1.4, it will force it to 24p, and likewise, some devices attempt to switch the monitor to 24hz if the source video is 24fps (eg film's that are encoded as such.)

3) If possible, connect all monitors and televisions by displayport. Windows locks all monitors to the same refresh rate, and on some cards that have a mixture of displayport and HDMI, using the HDMI port at all, will force all the HDMI ports to that refresh rate.

Like if you want to debug this, bring up the info panel on the TV/monitor when you see the frame rate drop and check if it changed the refresh rate on both. If it's changing the refresh rate, then the answer is the refresh rate is being locked across monitors. If it's not changing the refresh rate on both, then the answer is more likely the video acceleration is not being the dedicated h.264 ASIC on the nVidia card.

For what it's worth I have the same video card, different CPU, and have run the multi-monitor setup before (either on the iGPU or the nVidia card) and the h264 hardware acceleration that is flipped on depends on the order the codecs are provisioned by Windows. If you watch youtube or netflix in the web browser, open chrome://gpu/ you'll typically see "Video Decode: Hardware accelerated". You can try turning this off to see if it impacts anything, however I must express that anything you turn off in Chrome, will also turn it off in everything that uses nw.js (which can be considered a stripped down Chromium browser.)