The reason a larger round like the .45 is attractive in a smaller/shortened cartridge for military use is mostly so that it can be properly suppressed. In practical terms, any round designed for use in a truly suppressed ("silenced") weapon must
have its charge reduced in order to prevent the bullet from breaking the sound barrier. The sonic boom
(heard from the passage of a supersonic bullet as a CRACK
noise) is far louder than combustion effects on smaller bullets.
The problem with slowing down the round is that reducing the velocity reduces the bullet's energy, which reduces its effectiveness, especially at stopping (harming) humans quickly, which is what a silenced round is good for (no, they're not really any good for firing through cars or walls no matter what the movies tell you). One method of compensating for the lower velocity is to ensure that the bullet is as massive (in the technical sense) as possible, since of course energy is equal to 0.5 * mass times velocity 2 - increasing either of the two latter terms will work to increase total energy. While the slower, larger round will not perform as well at penetrating obstacles, this may not be what you want it to do anyway; a larger, slower round will transfer its energy more quickly and reliably to a soft target (such as a person) than a smaller, faster round which penetrates.
So, by allowing Glock to build small-frame pistols with higher stopping power, the .45 GAP might be used with the Glock 37 to replace the US .45 Special Operations pistol (which fires a regular .45 ACP, which can be and is downloaded to remain subsonic for suppressed use) - it's smaller, lighter, and probably more reliable/durable, all of which are Good Things in Special Forces' book.