I never had any issues streaming Construct games on Twitch. I think sometimes people don't quite realise how resource-hungry streaming can be, both in terms of internet connection and computer hardware, so I wouldn't be surprised if, in the past, people may have had issues.
But for reference, I was using Streamlabs OBS, capturing a screen and as far as I know, I had zero issues.
You can see the streams on our YouTube channel.