It doesn't serve up HTML, just an image.

    curl -v https://thisartworkdoesnotexist.com/
    GET / HTTP/2
    content-type: image/jpeg
    ...
    Warning: Binary output can mess up your terminal. Use "--output -" to tell

I'm pretty sure the server is just serving an image rather than an html file hence the lack of a source.

I tested this using Safari and Google Chrome and when inspecting the image element, both browsers produced different <img/> tags which I assume is because of the browser itself.

By serving a JPG file rather than an HTML document.

It's just serving an image.

Does it reimplememt a context menu?

Surely you can hit F12? Can't test on mobile.