Google play services doesn't get installed
You can download it from here, 
you need to search for your android version.
http://www.apkmirror.com/apk/google-inc/google-play-services/
you need to download for your android version>4.1/4.4/5.1/6.0
or try to reinstall YouTube

I have the same problem. 

I just download play services and problem was fixed. 

EDIT:they support android 2.3+ im using old android phone now,and I can confirm that they support ,also confirm that it's  working for 4.0.