I'm writing a game using node.js+express+socket.io. It took a long time to get where I am but i feel it finally got me. I have server which servs html and js files in this way:

app.post('/game', function(req, res) {
     handleGame(req, res); //it opens file using fs and forwards with res.end(readFile);
});

app.get('/scripts/*', function(req, res) {
     handleStatic(req, res); //same schema
});

And now, I'm logged and on site game.html (received from first app.post). It loaded fine, initRight is changed to 'bbbb', If I open 'source code' in firefox, I can click and see both player.js and game.js source code. Hovewer, inside init() Function of game.js module, there should be change to initRight field again to 'AAAAA', but as I can see Player function from player module is invisible inside game module (I've detected that when I was moving socket.io handlers to different module). I'm doing that in this way because I've seen it in different project and I really don't want next overwhelm with putting some require.js to get require() function etc. My question is should it work? If yes why it might not here?

While your question is confusing and I don't see the connection with NodeJS for your question, the problem is that your JavaScript has mutliple issues.

I copied your code to JSBin:

http://jsbin.com/iqudic/4/edit (and live: http://jsbin.com/iqudic/4)

Then, I cleaned it up a little bit.

You likely would want to put the associated attributes on the instance of the Player object rather than returning them as a new object like you were.

var Player = function(playerNick, playerId, playerSocket) {
  this.nick = playerNick;
  this.id = playerId;
  this.socket = playerSocket;
};

Secondly, and this was causing the AAAAAA to not appear:

function init() {
    // socket and socket.id should be defined before creating the Player
    localPlayer = new Player('AAAAAA', socket.id, socket);
    document.getElementById('initRight').innerHTML = localPlayer.nick;
}

Your code assumes that there is a socket.id and socket object available within the init function. It's crashing on that line. You should always take a look at the Console window of your favorite web browser.