I may be wrong on this one but I'm going to venture a guess to you as to where you need to add your code. I'm just learning this stuff but it looks like this is where it would go.

In your tpl_checkout_default.php file on line 36 it calls the tpl_checkout_stacked.php file which is where the single page with everything on it is located. I would venture a guess that you need an if( not a mobile user) { require tpl_checkout_stacked.php} statement here.

Again. I'm just a novice but that looks like it is the statement calling the page you don't want to be used into play. Hope it helps.