I think the big assumption (that is incorrect) is that his Bingo Card software is the only income for Patrick.
There is no reason you can't balance the "fun" work with other work that would brings in capital to continue building your vision. I'm doing that with my company. I'm building something that could be massive but right now I'm doing lots of web design projects to pay for the next business.
I also disagree that his Appointment Reminder software will be a small success. Patrick's bingo software is naturally a smaller venture. The market isn't gigantic. His Appointment Reminder software has a much larger market. If the average client pays $79/month, it would take ~1100 clients for him to be making a million a year. With his market, word of mouth will likely play a big role. I wouldn't be surprised if he had 1000+ clients at the end of 2 years.