For the tl;dr - Some hyperbole plus proof that the author doesn't understand very much about how an exchange such the NYSE or LSE works, how the financial system around them works or physical security and thus he comes the conclusion that it would be possible.

In real life though, it just wouldn't be possible.

1) Cutting all the connections to the exchange wouldn't be so easy. You're going to have multiple connections with different physical routes out of the building to minimize the chance that the exchange goes down due to a misplaced backhoe.

2) Assuming you did cut the connections, that alone would almost certainly trip the exchange's circuit breakers and halt trading. Even if the servers located at the exchange itself didn't halt trading, all the outside entities would lose contact and so you wouldn't get any trade confirmations back.

3) Even if you could execute the trades (somehow) clearing firms would almost certainly refuse to honor the trades as being legit, and if no one else is accepting that a trade got made, then for all intents and purposes it didn't happen.

tl;dr for my bit - No.