Even though the ST2 docs show that you can create a delayed task like how you are currently doing, you actually need to do it the following way:
var taskOne = Ext.create('Ext.util.DelayedTask', function() {
console.log('delayed task');
}, this);
Here are the parameters you can pass, you'll see I already included the scope above:
Parameters
fn : Function
The default function to call.
scope : Object
The default scope (The this reference) in which the function is called. If not specified, this will refer to the browser window.
args : Array
The default Array of arguments.
Good Luck!