StopOver/Layover Permit at PEK

I am not a national of any of the countries listed in the 72-hour Visa-Free countries.

But I read that there is such a thing as a layover permit for anybody wishing to go out of the PEK airport and has an outbound, booked seat to a 3rd country flight within 24 hours. Is this still available? I have an 8 hour stopover at PEK, and I was thinking that that might be enough time for me to visit downtown Beijing, but I do not plan to have to apply for an entry visa for this. The stopover permit seems like a great solution.