Great primary source quote!

So, to give you a little quick background info, during the early stages of the war, Union commanders were under strict orders not to disrupt Southern property unless it was deemed a military asset. The reasoning behind this was that Lincoln didn't want to agitate southerners any more than he had to by coming down there and acting like the brutish aggressor the northerners were made out to be. This would have been in 1861, when many people (Lincoln included) thought that it might be a quick war. With that in mind, and northern victory "assured," the notion was that northern troops and their generals should be as civil as possible to southerners to make the inevitable reunification that much easier.

All of this changed in short order, however. The war was not to be a short one, as we all know now, and no amount of chivalry and good intentioned manners could cull the Confederacy back into the fold. Union Generals in the field began to realize this as 1861 wound down, and one of them, Benjamin Butler, took the audacious step of confiscating southern slaves when he came upon them (or if they escaped and made their way into his camps). Butler did this by declaring them "contraband of war."

In this way, Butler (entirely on his own authority, and without permission from the President) went against policy and kept southern "property," which he justified by arguing that slaves, as property, were a crucial component of the Confederate war effort: just like wagons, cannon, or rail cars.

In many respects, Butler was absolutely right: in a lot of instances, the slaves were being used by the Confederate armies as menial labor (digging trenches and latrines, serving as cooks, teamsters, etc), which was indeed a valuable wartime asset. Although Butler was quietly scolded for over-stepping his authority at this early stage in the war (generals weren't allowed to alter official policy on a whim), Lincoln eventually came around to these very same conclusions. What's more, Lincoln also realized that even though the Emancipation Proclamation didn't actually free any slaves in the south, it did further incentivize those slaves to escape with the promise that in the north, they would be "free."

Also, as a political move, it knocked the legs out from under the Confederacy, for one of their best chances for actual independence was foreign recognition. With this move, Lincoln more or less assured that France and England would not side with the Confederacy.

So, how was it a military necessity? It gave the Union armies legal justification for confiscating slaves, it encouraged those slaves not near the front lines to make their way in that direction, further depleting southern manpower resources, and it acted as a political lever by which Lincoln was able to wedge Europe out of the conflict (for all intents and purposes).

[Sources: Bruce Catton, 'Glory Road'; James McPherson, 'Battle Cry of Freedom'; Shelby Foote, 'The Civil War: A Narrative, vol. 1 & 2']

The Emancipation Proclamation is interesting because it only freed slaves in the Confederate states, which Lincon obviously had no control over at the time. The idea was that as Union soldiers to back parts of the south, the slaves would be freed. But to answer your original question of why it was a military necessity, it was a matter of supplies. The slaves grew the food and other cash crops, which were vital to the war effort. No slaves = no work gets done. Basically, Lincon was trying to cut off the South's resources.