Do I qualify for the 72 hour free transit in Beijing

Hello,
I have a flight booked from Toronto Canada to Beijing (with a short layoff in Chicago on route on the way to Beijing). I will be in Beijing for less than 72 hours, and then have another flight booked to Seoul Korea. From Seoul, I will fly back to Toronto via Dallas. Will this qualify for the 72 hour free transit?

Am I correct that if I'm flying through Beijing I no longer have to notify the airport and can apply for the 72 visa at the airport?
Many thanks,
Shannon