Hello Analytics API: PHP quickstart for service accounts is not going to help you at all. That code uses the core reporting API the core reporting API is for requesting data from Google Analytics not sending data to Google Analytics.
To send data to Google Analytics we use the Measurement Protocol. The measurement protocol is used to send information to Google analytics the JS snippet you posted also uses the measurement protocol.
You can use the measurement protocol from any language that supports HTTP post or Http Get. That being said there is no PHP specific library for sending information to Google analytics you are going to have to format your post yourself. A tip would be to use Validating hits to check it before you send it to Google while you are developing this.
It will probably look something like this
http://www.google-analytics.com/collect?v=1&tid=UA-XXX-Y&cid=35009a79-1a05-49d7-b876-2b884d0f825b&an=My%20Awesom%20APP&aid=com.daimto.awesom.app&av=1.0.0&aiid=come.daimto.awesom.installer &t=event&ec=list&ea=accounts&userclicked&ev=10