The problem is that the gapi.client.load method takes a bit of time to complete, and it is asynchronous, so your page (which you've set up to be synchronous) is going on and running the searchA() method before the youtube library is fully loaded. There are two ways around this. One is to use the callback argument of the load method, like this:

<html>
<body>
 <script>
        function googleApiClientReady(){
                gapi.client.setApiKey('AIzaSyARvwirFktEIi_BTaKcCi9Ja-m3IEJYIRk');
                gapi.client.load('youtube', 'v3', function() {
                        searchA();
                });
        }
        function searchA() {
                var q = 'pink floyd';
                var request = gapi.client.youtube.channels.list({
                        part: 'statistics',
                        forUsername : 'GameSprout'
                });
                request.execute(function(response) {
                        var str = JSON.stringify(response.result);
                        alert(str);
                });
        }
 </script>

If you'd prefer, you could also wrap a promise around the loading callback:

<html>
<body>
    <script>
        googleApiClientReady=function() {
          loadApi() = function() {
                return new Promise(function(resolve,reject){
                        gapi.client.setApiKey('AIzaSyARvwirFktEIi_BTaKcCi9Ja-m3IEJYIRk');
                        gapi.client.load('youtube', 'v3', resolve);
                });
          };
          loadApi().then(function() {
                var q = 'pink floyd';
                var request = gapi.client.youtube.channels.list({
                        part: 'statistics',
                        forUsername : 'GameSprout'
                });
                request.execute(function(response) {
                        var str = JSON.stringify(response.result);
                        alert(str);
                });
          });
        };
</script>
<script src="https://apis.google.com/js/client.js?onload=googleApiClientReady"></script>
</body>
</html>