I believe the point he is making about "house money" and the Kelly Criterion is the size of the bet corresponds to how far ahead you are -- as you get farther ahead, your bets will get larger.
The problem with the comparison is that if you have one trader who started with $20, and another with $100, but they both currently have $50, they will both, by the Kelly criterion, be betting the same amount of money, even though once trader is trading with "house money" and the other is not. They're still trading without memory, which is the point that he was trying to refute, as I understand it.
The problem with the comparison is that if you have one trader who started with $20, and another with $100, but they both currently have $50, they will both, by the Kelly criterion, be betting the same amount of money, even though once trader is trading with "house money" and the other is not. They're still trading without memory, which is the point that he was trying to refute, as I understand it.