Prior to ECMAScript 2015 (ed 6), an object literal (ECMAScript calls it an "object initializer") key must be one of:

1. IdentifierName
2. StringLiteral
3. NumericLiteral

So you couldn't use an expression as the key in an initialiser. This was changed as of ECMAScript 2015 (see below). You could use an expression with square bracket notation to access a property, so to set the properties with an expression you had to do:

var required = { directories : {}};
required.directories[this.applicationPath] = "Application " + this.application + " does not exists";
required.directories[this.applicationPath + "/configs"] = "Application config folder does not exists";
...

and so on. Since this.applicationPath is reused a lot, better to store a reference to help with performance and cut down the amount of code:

var a = this.applicationPath;
var required = { directories : {}};
var rd = required.directories;
rd[a] = "Application " + this.application + " does not exists";
rd[a + "/configs"] = "Application config folder does not exists";
...

Edit

As of ECMAScript 2015 (ed 6), object initializers can have computed keys using:

[expression]: value

There is also shorthand syntax for property and method names.

See MDN: Object Initializer or ECMAScript Object Initializer.

Its nothing different and as easy as

var bob = {
    age:     30,
    setAge:  function( newAge ) {
        this.age = newAge;
    }
};

Alternatively, you can create a real setter function either by invoking Object.defineProperty() or as simple as

var bob = {
    age:       30,
    firstName: 'j',
    lastName:  'Andy',
    set setName( newName ) {
        var spl = newName.split( /\s+/ );
        this.firstName = spl[ 0 ];
        this.lastName  = spl[ 1 ];
    }
}

Where you could go like

bob.setName = "Thomas Cook";  // which sets firstName to "Thomas" and lastName to "Cook"