The comment is not "By signing up for Quantopian, you pay a membership fee to Quantopian, which is run by large trading firms."
The comment is "Large trading firms make money by being the counterparty of day traders making mistakes." When you mess up - which isn't just losing USD, it is underperforming the market's usually-positive return - there is someone out there on the other side of the trade who is buying what you sold and selling what you bought. When you underperform the market, they overperform the market by exactly as much.