“UDP streaming protocol” (although that will get you a lot of RTP type video streaming)
“UDP state replication” would work.
Read the code for the Quake games – it's open source, and fairly easy to read, assuming you know C.
Which technologies you use, depend entirely on what your game is.
If your game is turn-based and asynchronous, a simple REST system might be good enough. A game like chess is turn-based, but synchronous – time matters – and thus something slightly better is likely needed. If your game is a racing game, or a first person shooter, or an action-adventure, or a platformer, you probably need a streaming state replication approach, not request/response.
If your game HAS to be played in a browser, then you will need to use Websockets. You can “stream” over Websockets, but TCP head-of-line blocking when packets are dropped will cause lag spikes. There's nothing you can do about that.
If you have a mobile or native client, then UDP sockets are the way to go. On Windows, that's using the Winsock API. On MacOS and Linux and iOS, that's using the UNIX sockets API. On Android, you can choose between their “flavored” sockets (Java) or the underlying UNIX sockets API. Saying the sockets API is “old” is like saying that file I/O is “old” – it's a function, it's performed by the computer, it hasn't changed in forever.
That being said, for large scalability, you will want to use overlapped/asynchronous/evented I/O for your sockets on the server – but you're nowhere near the point where you need to worry about per-socket per-player overhead.
In addition to the Quake source, you can look for popular networking libraries for games, like ENet (C), Raknet (C++), or Lidgren (C#). Or run through the networking tutorials in the Unreal Engine youtube series, which will give you an idea of the higher-level concepts, and then you can map those to UDP sockets underneath.
Finally, influx, kafka, and pulsar, are systems to deal with streaming at the “seconds of latency” level, for bulk data. They are not suitable for a client/server networking setup for games, both because their latencies are way too high, and because their security models aren't suitable for the needs of most game networking setups. They can, however, be used on the back-end, for doing things like collecting metrics, or notifying “important” game events to central systems, or maybe even forwarding in-game text chat, at least if it needs to travel across server instances.