I am new to web development and want to design my first website to be compatible for desktops and all mobile devices. I saw the source code from another site that seems to have done this very well and they are using some kind of “screen webkit”.
I am wondering is this some kind of CSS that kind be found online? Can someone explain to me what they are doing with these “webkits” posted in the image?
Does anyone have any suggestions about what they are doing here?
I would like to do the same.
Thank you!

Webkit is a rendering engine. Safari, Chrome, Mobile Safari and the Android browser use it.
What you have there is a stylesheet with a media query. The stylesheet is only applied to browsers where any of those conditions are true.