Thanks for clarifying that. Leaving them blank and calculating on the partial matrices corresponds to putting zeros in all rows and columns of unplayed games. This method therefore, favours the games which get played the most. Thus I would prefer to keep the existing average rating method, which doesn’t favour the games which get played the most.
EDIT: Zarf has explained a slightly different variant (here) which allows for indifference and unplayed games. This method does not favor the games which gets played the most.