This game is called "Cluster"

Similar to Tic-Tac-Toe but Not Quite

  This game is basically a 3D tic-tac-toe, except that the rules have been changed to keep the first player from winning all the time. Here you have to form two rows that meet at a right angle (in the shape of an "L"). You play with blue marbles. Your opponent -- the computer -- plays with red ones.

   Click somewhere inside the grid to place a temporary (gray) marble. You can move it around by dragging it with the mouse. To rotate the entire grid, in order to get a better view, drag somewhere outside it. When you are satisfied with the marble's position, double-click and it becomes permanent. Then it's the computer's turn. And so on.

   The "Skill" buttons control how hard the computer thinks. Higher button means greater skill. Click the reset button (lower left) when you want to start over.