I have no idea what twitch is but your subscription entitles you to access the spotify catalogue for your personal use. I guess that, as long as music is in the background and not the main content of whatever you are broadcasting, there wouldn't be a problem but I'm not a lawyer. Full terms and conditions can be found here.
Bit of a grey area, technically it does breach section 8a since you are recording the stream:
Spotify respects intellectual property rights and expects you to do the same. This means, for example, that the following is not permitted: (a) Copying, reproducing, “ripping”, recording, or making available to the public any part of the Spotify Services or content delivered to you via the Spotify Services, or otherwise any making use of the Spotify Service which is not expressly permitted under these Terms