https://www.twitch.tv/p/affiliate-agreement

Let's see here:

starting from beginning of the Initial Broadcast of any Live Video Content, and continuing for a period of twenty-four (24) hours following the end of the Initial Broadcast of such Live Video Content (the “Exclusivity Period”), such Live Video Content is exclusive to Twitch (even as to you)...

Yup, the live broadcast from beginning to end plus 24 hours after the end of the broadcast is the "Exclusivity Period".

During the Exclusivity Period of any Live Video Content, you will not, nor permit or authorize any third party to, broadcast, stream, distribute, exhibit and otherwise make available such Live Video Content in any manner. Notwithstanding the foregoing, you have the right to make any Live Video Content available, during the Exclusivity Period, solely via the Twitch Services.

I take this section to mean that the video cannot be made available on any other service except Twitch during this "Exclusivity Period". I believe that you can upload content to YouTube without making it available for consumption using the Private setting. However, I would add that since the video can still be shared via email, the onus is on the user to not break the Exclusivity Clause. This is only my interpretation though.