Twitch is now allowing users to access Video on Demand content on their mobile devices. On the activity feed on any channel you can find the on-demand content as long as the channel owner has made the live streaming available for their content and you can see past videos on a smartphone or tablet.
Tapping on any offline channel will take you to an activity feed where you can also search in the in-app search page for VOD content. Content such as game play and Twitch Weekly can be viewed on-demand.
Additionally Twitch is asking Android users to download an entirely new app. Security issues have forced Twitch to develop an all-new app available via Google Play. Updating the old app will not fix the problem. There is no info to what the security flaw may be.