however if you do have a significant number of moves in a game, it will help to have an index on the order by column, so that may be something to keep in mind down the road.
One thing I remember is that Oracle would ignore an index for an order by, even with a hint to the optimizer, unless you add a do-nothing comparison, e.g. "... and move_number > 0" to the where clause. Don't know if PG is dumb the same way.