document.addEventListener("DOMContentLoaded", function() {
initialiseMediaPlayer();
}, false);
Will execute initialiseMediaPlayer when the dom content is loaded.
document.addEventListener("DOMContentLoaded", initialiseMediaPlayer();, false);
is a syntax error; if you remove the semicolon:
document.addEventListener("DOMContentLoaded", initialiseMediaPlayer(), false);
calls initialiseMediaPlayer immediately, then passes the return value (which likely isn't a function) to addEventListener. This won't act as desired.
You can do
document.addEventListener("DOMContentLoaded", initialiseMediaPlayer, false);
(remove the parentheses = function call). Then initialiseMediaPlayer will be executed on dom content loaded, and act as desired.
However, unlike in the former case, initialiseMediaPlayer will actually receive the arguments given by the browser. Also, its return value is received by the browser. In case of DOMContentLoaded, most likely this doesn't matter much.
You also avoid creating one extra anonymous function if you pass initialiseMediaPlayer directly. Again, the effect is not really perceptible from the user's standpoint.