Does normal javascript works on node - webkit or not?

Yes, normal Javascript works on Node webkit.

Node runs a Javascript V8 engine, so any JS function will be understood in Node.

Your error is the following :

var asd = document.title; //This is a string

setTimeout(asd(),1000); //You call asd as a function, which does not exist, hence the error

EDIT :

With the new variable name, that should work :

var blinkOrder = 20;
var blinkNumber = 12;
var asdf = document.title;
function asd(){
    if (blinkNumber >= blinkOrder) {
        document.title = ' hi';
        blinkNumber = 0;
    }
    else{
        document.title = asdf;
        blinkNumber++;
        setTimeout(asd(),1000);
    }
}
asd();

Even though I understand the downvotes, I would like to add this answer :

Be careful with hoisting (http://www.w3schools.com/js/js_hoisting.asp)!

Functions and variables are hoisted, but functions take precedence is JS in hoisting, so asd, in your code, is first assigned the function, and then the document.title value.

console.log(asd); // asd(), because even if the function is defined further
                  // in the code, it is hoisted
var asd = document.title;
console.log(asd); // document.title value, so the string of the page title
function asd(){
    if (blinkNumber >= blinkOrder) {
        document.title = ' hi';
        blinkNumber = 0;
    }
    else{
        document.title = asd; // Why ??!?!
        blinkNumber++;
    }
    setTimeout(asd(),1000); // setTimeout() is expecting a function reference!
}
asd(); // Here, asd has been assigned the document.title value, and a string, not being a function, cannot be invoked, thus the error thrown.