Inference is (mostly) stateless. So unlike training where you need to have memory coherence over something like 100k machines and somehow avoid the certainty of machine failure, you just need to route mostly small amounts of data to a bunch of big machines.
I don't know what the specs of their inference machines are, but where I worked the machines research used were all 8gpu monsters. so long as your model fitted in (combined) vram, you could job was a goodun.
To scale the secret ingredient was industrial amounts of cash. Sure we had DGXs (fun fact, nvidia sent literal gold plated DGX machines) but they wernt dense, and were very expensive.
Most large companies have robust RPC, and orchestration, which means the hard part isn't routing the message, its making the model fit in the boxes you have. (thats not my area of expertise though)