Yes ! PSVITA is alive !
It’s been very long since a new app is released for PSVITA / PSTV , but today Twitch is suddenly became available for both PSVITA and PSTV ( finally a steaming app for PSTV ) and you can download it from the store from here
This app features :
+ Live and recorded video of top games, players & esports events
+ Ability to follow channels and games you want to keep tabs on
+ Special section to highlight PlayStation® broadcasters