Do I need China Visa for Beijing cruise to Japan round trip from Beijing?

I am US Citizen living in San Diego, California. Plan to visit Korea and flying round trip from Seoul, Korea to Beijing to get on a five day cruise round trip from Tianjin to Japan. We don't plan to stay in Beijing before or after cruise, but our departure and arrival flight from Seoul to Beijing 6 days including 5 days cruise. Does 72 hour free transit apply to my case since we stay less than 72 hours in Beijing.