#JavaScript, 360

As requested, text based game, input via popup, output in console (so to have a monospaced font).

Quit game with 'q' or clicking 'cancel' at prompt.

Not using ES5 features, it should run on any moder browser (where you can have a JS console panel)

<!-- begin snippet: js hide: false -->

<!-- language: lang-js -->

    b='\n......'.repeat(6).split('');
    for(h=t=0;!h&t<36;)
    {
      i=prompt();
      if(i=='q')i=null;
      i=i.match(/([0-5]) ([0-5]) ([XO])/);
      m='INVALID';
      if(b[p=i?i[2]*7-~i[1]:0]=='.')
      {
        ++t;
        b[p]=i[3];
        m=b.join('');
        for(x=z='',c=0;c++<6;)
          for(x+='_',z+='_',r=0;r<6;r++)
            x+=b[c+r*7],z+=b[c<4?c-1+r*8:c+1+r*6];
        h=(/X{5}|O{5}/.test(b.join('')+x+z))
      }
      console.log(m);
    }
    console.log("P"+(2-h)+" WINS")

<!-- end snippet -->

**Now, some more fun** Interactive and graphic version, run snippet to play.

<!-- begin snippet: js hide: true -->

<!-- language: lang-js -->

    b='\n......'.repeat(6).split('');
    t=0
    sel='X'

    function show() {
      var w,p
      p=t&1
      $('#B').addClass('OC'[p]).removeClass('CO'[p]);
      w=b.map(function(c,i){
        return c>' '?'<td class='+(c=='.'?'F':'X')+' id=C'+i+'>'+c+'</td>':'</tr><tr>'
      }).join('');
      $('#B').html('<tr><th colspan=6>Playing: '+(['Order','Chaos'][p]) + 
      '</th><tr><tr><td colspan=6>' +
      '<input type=radio name=S value=X' + (sel=='X'?' checked':'')+ '>X '+
      '<input type=radio name=S value=O' + (sel=='O'?' checked':'')+ '>O</td>'+
      w +'</tr>');
    }

    show()

    $('#B').on('click','td.F',function(){
      var x,y, p=~~this.id.slice(1)
      x=p%7-1
      y=p/7|0
      sel=b[p]=$('input[type=radio]:checked').val();
      ++t
      for(x=z='',c=0;c++<6;)
          for(x+='_',z+='_',r=0;r<6;r++)
            x+=b[c+r*7],z+=b[c<4?c-1+r*8:c+1+r*6];
      if (/X{5}|O{5}/.test(b.join('')+x+z))
      {
         alert('P1 (ORDER) WINS')
         b='\n......'.repeat(6).split('');
         t=0
      }
      else if(t==6*6) {
         alert('P2 (CHAOS) WINS')
         b='\n......'.repeat(6).split('');
         t=0
      }  
      show()

    })

<!-- language: lang-css -->

    th {
      font-size: 12px;
    }  
    table.C th {
      color: #807;
    }
    table.O th {
      color: #087;
    }

    td {
      font-family: monospace;
      font-size: 12px;
      width: 1em;
      height: 1em;
      text-align: center;
    }    

    table.C td.F:hover {
      background: #f0e;
    }
    table.O td.F:hover {
      background: #0fe;
    }

<!-- language: lang-html -->

    <script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
    <table id=B></table>
    <p id=O></p>

<!-- end snippet -->