Is it possible to see how many page views a web page gets - for example, this article - without having access to the page’s code? Like some script of something that I can run that says “this page has x viewers since you last checked” or something?
No, you cannot do that without access to the server the site runs on or the network on which it sits.
Any arbitrary website? No.
Your own website? You would need access to the code at least once, to add a script to the page (e.g. Google Analytics or a page counter). After that, you wouldn’t need to modify anything to check.
Thanks. And yes, I meant any arbitrary website.