I sideload my own books and then turn off the internet on the Kindle. Other than knowing what books I have, are they still able to monitor all those other things?

I ask because I don’t completely understand some of this internet networking stuff. The other day I turned off my router while I was watching a video on YouTube and the video kept playing with no interruption or lag while I thought I had turned off the wifi in my house. I guess we can’t turn it off anymore? Or was it able to keep playing because it was cached?