Error: no client id specified - but it is

API
2

Should be, as multiple parameters need to be seperated by & not ? for each one

https://api.twitch.tv/kraken/search/channels?query=starcraft&client_id=lxk3o4wydpchvpocy11f6ia862upux

and you really should be specifying it as a header

https://dev.twitch.tv/docs/v5/guides/migration

as currently you are also missing the required v5 header