In your move()
function you should do something like
if (x >= dest_x) {
alert('player 1 won');
} else if (x2 >= dest_x2) {
alert('player 2 won');
} else {
... continue the loop ...
}
You'd most likely put that behind
document.getElementById("cowboy").style.top = y+'px';
document.getElementById("cowboy").style.left = x+'px';
document.getElementById("cowboytwo").style.top = y2+'px';
document.getElementById("cowboytwo").style.left = x2+'px';
You might want to check your code on duplicate variables too, by the way.
AFAIK dest_x and dest_x2 are both the same for example.