Any ssh client can log in remotely and issue a log out or shut down command. Linux, Unix and macOS all ship with ssh. Windows, try the putty program.
ssh user@hostname
sudo shutdown -h +25
The shutdown command with +25 would be for someone that paid for 25 minutes and the machine shuts down unless it’s cancelled. You can get as fancy as you with with AppleScript or making a process to read a value from the controlling computer. It all depends on how much money you want to spend and how much reading on the free tools you like to do to get a few details correct.
If you wanted to buy software to help you manage all these Macs, I would start with Apple Remote Desktop.
You’re going to need to manage which apps you install, update the OS, make new user accounts for the clients, change settings to enable guest mode, etc…
Managing their sessions is just the start for your business to work. If you have more money than time, you might choose an MDM to automate things further and let a programmer help with the billing software to integrate with how long each session is and not need Apple Remote Desktop eventually based how much MDM you do. Probably you wouldn’t invest in MDM until hundreds of Macs need managing or you set this up for a chain of cafes.