Grim's comment is along the lines of having highlights, segments, snippets from games. Not complete games.
King's comment specifically refers to highlights as well not complete games. Most TV stations 'morgue' the nightly game highlights that they use during the newscast for use in the future. (i.e. if a player is traded, signed or if a former player passes away for example...)
That is what they are used for after being shown the night of that particular game.
The reason there are radio broadcasts available is because that was the main format in use for over 40 years basically before TV really became popular. Audio tape requires storage and protection but not to the same degree as film.
Also Bob Grim told me that MLB now requires that a copy of every game be sent to league headquarters for storage.