Video streams can be extremely CPU or GPU intensive, depending on the codec, bit rate, even the content being streamed. A gaming PC isn't going to feel it, but read reviews of older netbook pcs, they talk about its video decoding capabilities. As to why they would "suddenly" have issues, they've never needed to do the encoding on their end and decoding on your end in a matter of milliseconds. Sure, video decoding is easy these days. If you don't care if your video stream is delayed by a few seconds, like happens with Twitch, YouTube, Netflix, etc.
Just today I was watching a live auction on Twitch (DesertBus!), and you could clearly see the video lag, reading chat was like reading the future. You would see "Going Twice!" in chat and then 5 seconds later in the video "We're going twice!"