For reference, @jollyok, I tried this on my supported Pi-hole and, even with Pi-hole blocking disabled and browser ad-blocking disabled I can't see any video and the buttons don't respond to clicks, so it appears to be a problem with that page. I used Safari, so perhaps if you did too then they have made assumptions in the page setup which aren't valid on this browser.
I see, yes. It loads all kinds of material from all over the place. You can use Firefox's developer console to help find out where it is all coming from and whitelist the relevant domains. There's a player applet, the content and so on. See the link below for the general idea.
For any Pi-hole-specific support contact the providers of the variant you're using, or deploy the official version on a supported platform.
I use a combination of Pi-hole and a browser-based ad-blocker extension. If I disable both and clear the cache and cookies for that site and load it up it works okay. If I have them both enabled (the default) then the site behaves as you originally described. I see a lot of domains in Pi-hole's Query Log, and a network view of the page loading in the developer console shows all kinds going on, so something is blocked and the page doesn't like it.
This is a standard thing you can see on some pages when using DNS and/or a browser-based ad-block extension. The link above, and the browser's developer tools, can be used to track down the important domains or content so it can be whitelisted where possible.