What plugin or app is this website using to display these last minute appointments?

I am trying to create a website similar to this, but for salons; connecting hair stylists with people who are looking for last minute appointments. The calendar app is not really useful for this because it’s not just one company’s schedule that I need to display, it’s multiple. I thought of tables, but I need it to automatically update with the new appointments and that is where I’m stumped. Help?