Well, i really don't get it.
Causes way too much stress on the viewer, who's probably watching in browser window anyways, and the transcoding for lower qualities is sub-par.
lagfree gaming without second streaming PC is almost not possible, if you want play on the highest possible graphicsettings and even use 1080p60fps in stream settings, still different which game you play and i didnt know how good the new nvidea graphicscard will working^^
His new one could easily handle common stream quality in the background. Also keep in mind he wanted to use his old PC for this purpose.
Btw, why are you so focused on 1080p60fps?
General support of Win7 ended 14 months ago, security patches will still roll in for the next 4 years.
I'd go for Win10, especially considering gaming (DX12).