The big organisations probably run something enterprise-grade on AWS or Microsoft Azure where you can spin up hundreds or thousands of virtual servers to run your application and deal with spikes in traffic and workload. Of course, all for an appropriate cost. Running services on these platforms is a skill in itself as they're highly complex and certified consultants who understand them cost big money.
Also, you'd have to do some analysis on the predicted numbers of users as well as the type of server workload required for your game in order to determine what type of computing, networking, database, and storage resources you'd need and design your application and infrastructure in a way that supports parallelism so you can scale out as it grows.