@cgty 

I don't know how TP-Link's website blocking works, but if it's done via DNS filtering, then you might want to check which DNS server is specified on the Chromebook. In case there are more (or other) name servers specified than just the IP address of your router (normally 192.168.0.1 unless you've changed it), then this could be a reason why the blocking doesn't work.

Furthermore, computer operating systems also have what's called a "DNS cache", which retains information of recently visited websites. So it's possible the router does properly block the DNS requests for youtube.com, but the Chromebook then just uses the information it still has in its DNS cache to get the IP address of youtube.com. If you want to rule that out as well, then you need to "flush" (erase) the DNS cache. 

@woozle IDK how TP-Link's website blocking works either, but obviously not very well. I know about DNS caching; I have rebooted the chromebook mutiple times (which will clear the cache), but the problem still persists.

@cgty facing same issue. Did you resolve it?

@imauser no I didn't - I ended up setting up a https://pi-hole.net/ ubuntu box, and using that to control the site access. Low cost, but requires some extra tech skills.