8.8.8.8 isn't a youtube IP, it's Google's DNS service. Most networks hand out their own DNS and generally expect clients on their network to be using it. While most consumer home networks are very permissive not every network is and not respecting the dns server handed to a client by DHCP is broken behavior.
I adressed these points already in other places through this thread: Why would it be any different if they just hardcoded the IP to YouTube? Would that also be "not respecting the DNS server from the DHCP client"? What if they used a proprietary protocol (not DNS) to look up the IP to YouTube?
Just because your network provides a DNS server does not mean that it makes sense to use that DNS server for every single IP address lookup in every piece of software. It's there for general internet browsing purposes, not specialized proprietary purposes like this.
