First some questions.
Will it always be just 9 products? Or are you likely to ever expand to 15, 50, 100 or 1000 products?
Is it just the slider of products you want like in the video, or will you want individual prodct pages too?
I have not time to watch the whole video, but I guess that is showing how they did the slider. It’s not just going to be server-side PHP, that is mostly client-side HTML/CSS/JS. PHP will just dish out bits of HTML for each item from however you are storing the product info.
How you store the product info will depend on the above questions; if you don’t already have that sorted.
You can build your layout manually with HTML/CSS/JS and simply add buy now buttons to each item. This means that if you ever need to add new products, you will need to manually add them into the page with code. But it will get you up and running quick. In the future, if you see a need, you can the site to use a full-blown CMS that could make managing products easier.
If that is the case and there will be no significant expansion of the product range then you probably don’t need to get into using a database.
Instead you could, as Joe says, manually code the product slider in HTML without a lot of PHP, adding the CSS for styling and JS for interactivity.
Alternatively if you wish to partially automate the rendering of the slider, you could store product info as an array of objects (either JSON or PHP) and have the slider generated from that. Which may be more difficult to initially set up, but will make for less work if you do end up changing the product range in the future.
Where you will need the server-side is managing the basket and checkout. But that’s a separate concern from initially creating the product slider which is more of a client-side thing. So take it one step at a time. But again, having a single record of product data in one place will help with managing both parts and reduce repetition sice they need access to the same data.
There are lots of pre-built “carousel sliders” available online, like Owl Slider etc. They usually have instructions for how you can add them to your web page. Before doing so, though, read up on the pros and cons of this sort of layout. I’ve read stats that suggest people don’t like sliders and that they don’t use them. There are nicer ways to lay out products, such as in a nice clear grid so that people can scroll naturally and view the products easily. Don’t just choose a slider because you think it’s cool etc. They’re actually awful.
I would argue that’s a reason NOT to use a slider.
If you have few entries to link, you want all of the entries visible and… for lack of a better term… filling space. You dont want to hide the articles you do have inside a slider.