On these old computers everything other than video decoding was accelerated (though, partial or full MPEG2 hardware decoding did exist as well). YUV to RGB conversion, scaling (to e.g. 1024x768 or 1280x1024, modulo letterbox) and maybe something I'm missing ; it was the Overlay mode. No wasteful copying to memory of the scaled video either (just display it). I believe it still exists and is still used in standalone video players (otherwise, there are DirectX, OpenGL etc. output paths).
The S3 Vision 868 and S3 Vision 968 graphics cards could do that. They were available in PCI and VLB versions.
But for some reason web browsers cannot use or don't want to use that, and I've spent a decade complaining to strangers on the internet lol (or trying to convince acquaintances/friends to download not stream, or listen to music in other ways than with the youtube website)
There might be odd limitations with overlay mode. But anyway, if the video rendering is fully accelerated (typically with H264 codec and up), then the browsers do support that and any bottom of the barrel, outdated phone/tablet significantly worse than Atom N270 and friends can do 1080p decoding and playback without breaking a sweat (720p if too old/limited)
/edit :
I remember now, that when you took a screenshot of your windows 98 desktop etc. with a video playing, the media player window would not show the video, it was blank/fully black. Spooky.