I'm not sure why everyone is complicating the situation with their answers... it's a simple case of using indexOf on the wrong variable...
This line:
console.log(myArray.map(function(f){ return f.substring(myArray.indexOf(" ") + 1);}));
Should be:
console.log(myArray.map(function(f){ return f.substring(f.indexOf(" ") + 1);}));
You want the index of the space inside the current string that you are checking, but you were calling indexOf on the original array, which of course returns -1 because the value is not found.
Additionally, if you want the output to be exactly like your expected output statement, you will need to use .join() on the result:
var myArray= ['This is', 'a game', 'worth playing'];
console.log(myArray.map(function(f){ return f.substring(f.indexOf(' ') + 1);}).join(' '));