What does meaning really mean? Generally it translates as resonant, illuminating, symbolic or significant. In some cases all of the above. A meaningful song might evoke the history of a revolution for the listener, so that even though she does not know the facts she feels a connection to it. The same is true of novels, movies and art.
Games incorporate agency and so many of the events that happen within them are of a player's making. An action causes change in the game world, and can therefore be significant, but not necessarily resonant, symbolic or illuminating. The question for games is really whether they can incorporate other kinds of meaning too.
I think they can.