In the first step, he says roughly "assume half of the nodes change protocol". I named by dog Bitcoin too but he doesn't have the same UTXO state as the main chain.
If Alice changed the ruleset so drastically, I don’t think she could find any Bob that would be willing to accept this thing as Bitcoin. But maybe the probability is not 0.
If Alice only changed 1 little rule and made it conflicting with the ruleset used by the rest of the network, it’s easy to imagine consensus failure and being able to find 1 Bob that gets tricked into receiving a double-spent Bitcoin. In fact, such a system failure has happened already in 2013, when for 24 hours no one knew which ledger was the real bitcoin: https://bitcoinmagazine.com/articles/bitcoin-network-shaken-...
