The past little while, I’ve noticed a very annoying feature on both Chrome and Safari - when I’m browsing a news item in text, a pop-up video often starts with a newsreader reading the same story.
I don’t want that.
Is there any way I can turn it off?
The only thing that has worked for me is using an adblocker such as Ublock Origin to permanently block the popup.
For both Chrome and MS Edge there are extensions you can install that pretty well stops those. There are many such to choose from, but I use this one and it works well for me.
I have no Safari experience, but it’s a decent bet there are similar extensions with similar functions.
Unless there is something weird on your computer, it has nothing to do with Chrome or Safari, and everything to do with certain news sites. They seem to want those video views.
They nearly always have a video on the top of the page that starts playing, and then changes into a popup as you scroll down. So anything that stops the videos from automatically playing should stop them.
So, yes, extensions like the one @LSLGuy mentions should help. But you’ll need to allow autoplay on sites where you actually want the video to autoplay. Most people like autoplay on video websites.
I don’t like videos, or auto play. 
Me neither. I will decide whether and when to make a vid happen.