Twitch isn't real time.

Yes it is. The delay on a Twitch stream doesn't mean they don't have to deal with encoding and transmitting frames at full speed. If Twitch wasn't real time, you'd only be able to watch live streams slowed down!

That's a different definition than most people mean when they say "real-time".

Not me. All realtime systems have some latency, but what makes them realtime is that they must maintain throughput, processing data as quickly as it comes in. You can subdivide to hard-realtime and soft-realtime depending on how strict your latency requirements are, but it is still realtime.

really? I think not. Lets use speech synthesis as an example: I would call speech synthesis real time if it takes less than one second to produce one second of synthesized speech. I think you're probably thinking of the word "live". There's always going to be a small delay when re-encoding. Real time doesn't mean 0ms delay, that's impossible. Twitch has a small delay, but it's still re-encoded in real time (encoding 1 second takes ≤ 1 second for twitch).

The delay (configurable) isn't due to the encoder. And the encoder has to process everything in real time, otherwise you start skipping frames or fall behind.