Mh well... The first thing to know about SEO is that basically noone has any idea how google (and other search engines, I'll just use it synonymously for all search engines because... come one ) actually rate websites. It's a well kept secret because if everyone knew how to be the best, well... what's the point of having a rank then. Only a few things are known, and even on those it's unknown how heavy the impact is.
Google looks for a lot of stuff on a website. They pretty much stopped looking at keywords in a website years ago, there was too much abuse, so don't bother with it. They look a lot into the structure of the data.
You could look into the semantic elements in HTML5, those supposedly help a lot in rating. Following proper heading sizes also falls into semantics. If you look at the source code you'll notice that all h1 and h2 headings are static, h3 are the first in the hirarchy that change (because they are article headings) and so are rated higher, hence in the search result.
If you look into the actual source code of the main page you'll notice that those links are not in the meta tags (especially look for the "Fastest Ryzen System" thing).
My guess is that they also take page visits into account on those links if you're using analytics, but take that with a grain of salt, because... it's a guess
It also helps when your site is responsive and therefore mobile friendly. They started dropping ratings for non-mobile friendls sites a few years back, so if it can be responsive (and there's not really any reason to not have a responsive website these days) it should be. If you're developing from scratch anyway it's a nobrainer. Just remember that using device-specific breakpoints is kind of a bad practice, you should place breakpoints whereever your site looks broken.
What google also doesn't like at all is when you display completely different content for different devices (or even worse, just the crawler), you should rather place a redirect to another domain or just do it via responsive design.
Depending on the site you are doing you can also influence snippets on google a little bit, using microdata in the page. There are a few ways, OpenGraph and Schema are the most used though. Both work, but the approach is different. OpenGraph was initiated by Facebook and also impacts heavily what is shown on a link in social media channels (or even skype or discord these days), or even this forum (see the OGP link below) . Schema is primarily supported by google/+. You can of course also combine the both. Twitter also has its own thing, but they fall back to open graph data if none is available.
I personally prefer Schema, because the data is not duplicated, but right on the element where the content is, it can be a pain to implement though. The biggest issue you'll always be facing is the content editors, because they need to be aware of it and actually use it. It's easier for automatically generated pages of course.
What you can do in addition is also generate a sitemap, there are a few guides on googles helpcenter about it (or at least were a while back) to point to the "most important" links, with that they may be displayed as sub-links right under the search result, with a little indentation (I don't have a screenshot right now, but I'm pretty sure you've seen this before).