Hi @Awesomegamer656. I've been streaming to Twitch directly from my Pi, going directly from the emulator like you have. It has worked for NES, SMS, Genesis/Megadrive and MAME and FBA, but for some reason it doesn't work with PCEngine. I haven't personally tried NXEngine (not even sure what that is, honestly) but there is another way, which is what I did to stream PCEngine.
Start up a game as normal, without the Twitch streaming custom emulator and hit Select + X to get into Retroarch. Go to the Quick menu and Settings and Recording and you can enter the Twitch link with stream key there. Then go back to main menu and you should see Start Streaming, and then it should be on your Twitch.