On one specific computer or on all computers/network devices?
What network connection are you using: wired, wireless?
More information is needed.
Open Task Manager to observe what your system is doing for a few minutes. Slide the window to the side but leave the window open.
Then watch the same YouTube videos. Could be the system is trying to do some backup, an update, or AV scan.
Everything slows as some resource is being overloaded.