There's absolutely no
reason to use anything better than that! Hell, I built my mom a "new" PC (which she uses as an HTPC) because she got a Sony 4K OLED TV and the Phenom II X4 940 system with an XFX Radeon HD 6450 couldn't handle 2160p.
I built her a PC using spare parts I had lying around. Her CPU is now an FX-8350 on a Gigabyte 990FX motherboard with 8GB of Cetus UMAX DDR3-1333. For her GPU, I gave her what was the direct rival of the GTX 980, a Sapphie R9 Fury Nitro OC+. I also bought her a Gigabyte P650B 650W 80+Bronze PSU (on sale for $40CAD), a new case to fit the gigantic (307mm) R9 Fury (about $50CAD) and I grabbed her a 128GB 2.5" SATA SSD to use as her system drive.
As an HTPC running Windows 10, it is literally PERFECT. There is literally no upside to buying new hardware for an HTPC when the hardware that you have would be more than sufficient. Put that extra money towards upgrading your gaming PC because otherwise, that older hardware you have will just become more e-waste before its time.
I know that you like newer hardware, I like newer hardware too but you gotta remember that hardware advancement outpaces software by an order of magnitude. There will be literally no benefit whatsoever to be gained by buying new hardware for an HTPC because your HTPC will be at least
as good as my mother's and as I said, hers is PERFECT.
All I'm saying is that you should at least try it out before you piss your money away. I know that if you do try it out, you'll be more than satisfied with it and that's hundreds more that you can dedicate to upgrading your gaming PC which is pretty significant. The money that you spent all those years ago can still be of great benefit to you. Since you've already spent it, you might as well, eh?
There will be no difference whatsoever in media playback (even at 4K) between a GTX 980 Ti and an RX 6600 XT. They will both play whatever you want with perfect clarity without stuttering. The difference is that you already own the GTX 980 Ti and it's not like you're ever going to have to worry about driver updates for media playback. If the card kicks the bucket down the road, then sure, replace it. Until that day though, it's a complete waste because nobody's in the market for a card that old for more than $50.