the blockchain is confirmed through the internet. it's the ledger that says "so and so address (which means wallet) has this amount of BTC." without the internet, BTC would be worth nothing.
Here's where I'm coming from. Usenet, and FTP, as well as MIRC, are separate protocals from Http. Email is a different protocol, too.
When I think of Internet, it is http and https. These protocols may be useful, but are clearly not required to maintain the blockchain or verify it.
But perhaps when they use a phrase like "Internet Kill Switch" it means shutting all this stuff down.
For me Internet is TCP/IP, with dash of UDP and handfull of others... Okay it's a real mess when you get in too deep. Just look at the wikipedia...
There is two alternatives for "Internet Kill Switch", one is the DNS-system and the other one is lot of inter network connections...
First case isn't impossible to handle, second one is rather deadly.