Ticket is not a connecting ticket for 24 hour transit visa

Massilia, you are definitely and undeniably eligible for 24 hour visa free transit because separate tickets are and they always were acceptable. Also, using separate and unrelated airlines is and always was acceptable.

The only thing you will have to accomplish is the obtaining of the temporary entry permit when you land in Beijing. The first thing you will do is to approach 24/144 hour visa free transit counter where you will apply for a temporary entry permit in order to be allowed to exit the airport, to collect your luggage and to perform your new check-in for your flight to Riyadh. This application is free of any charge and here you will present your flight tickets. After a short check, you will be granted a permit and you will then head to the immigration.

When you are done with the immigration, you will collect your luggage, perform new check-in and head again to the immigration in order to catch your flight to Riyadh. Remember that this is your right and something like this is visible in Timatic if the staff at Tokyo airport finds relatively uninformed about this scheme. Just persist, this is your right. Have a nice journey.