Surely it wouldn't normally be written into the HTML? Or is this actually what you normally get if you use a website builder, or get someone else to do it? (My only experience is of coding my own webpages.)
What your browser displays is HTML. So whatever you see on your screen is somehow in the HTML that's served to your browser and/or generated dynamically as you're viewing the page. The question is how this HTML is generated. This can be done in a static way as we did in the 1990s, and it's indeed how most of the main content of ublinkingeye was originally made. However, in that static content there's also in this case a number of places where dynamic content is embedded.
Now, I've paused my adblocker and refreshed the website a number of times and I don't get any gambling ads, but that may be due to the fact that those are illegal presently where I live, so I'm less likely to get that sort of content. Which means I can't reproduce the Russian gambling ads stuff you seem to be seeing, but to give an example, let's have a look at this bit of embedded content:
As you can see, it won't render for me, possibly for the reason indicated above. Let's have a closer look at the white iframe with the error message:
HTML:
<iframe style="width:120px;height:240px;" marginwidth="0" marginheight="0" scrolling="no" frameborder="0" src="//ws-na.amazon-adsystem.com/widgets/q?ServiceVersion=20070822&OneJS=1&Operation=GetAdHtml&MarketPlace=US&source=ac&ref=tf_til&ad_type=product_link&tracking_id=unblinkingeye&marketplace=amazon®ion=US&placement=2880467144&asins=2880467144&linkId=bdef1605ce4d0fdbd389490cfc81aec9&show_border=false&link_opens_in_new_window=false&price_color=333333&title_color=0066c0&bg_color=ffffff">
</iframe>
As you can see, this iframe is supposed to populate itself with content from Amazon's ad system. It's possible that in your case, the content renders fine and in that case, it would also pop up in the DOM which you're inspecting using the 'inspect' function (or similar) in your browser.
There is typically waaaay more than HTML driving a modern website.
Well, yes. But the HTML as such really isn't the thing; that's just the stuff that shows up. What happens under the hood is where the complexity is. In part this is client-side processing that happens mostly in JavaScript, which you can trace down and dive into if you have plenty of time. But there's also generally a lot of server-side processing going on; sometimes this results in quasy-static content being served (classic PHP generated server-side, for instance), but today, most websites use 'live' content with the browser continuously interacting through something like e.g. AJAX with a server backend. The frameworks used for this can be exceedingly complex and only a small part is visible to the typical end-user (which of course is by design).