The simple answer is that the newspaper got lucky with an attention grabbing headline. The battle did end up becoming significant as a turning point in the war, but I don't think its true significance would have been apparent the same day of the battle. In fact, the military value of the victory was greatly reduced in the next few days when Meade hesitated in pursuing Lee after the battle, allowing him to escape with his army largely intact.

The most important outcome of the war was more psychological, and took a bit of time to manifest. First was to prove that the Union Army had finally found a general who was capable of going toe to toe with Lee and the Confederates. The Union had gone through five commanders, who all either lost or failed to decisively defeat the Confederate military even when outnumbering them 2:1. This reassured politicians, commanders, and Union soldiers that they could actually fight and win. Meade's failure to pursue actually dampened down a lot of the post-victory enthusiasm, but a win was still a win.

The other affect was on the Confederacy to break the image of the invincible Lee, and the Confederate soldier who could whip five yankees by himself.

Had Meade caught Lee and scattered his army, as Lincoln and others expected him to, it would have certainly lived up to victory at Waterloo.

Edit: Whoops, yes, Grant at Vicksburg, Meade at Gettysburg.

While a very enthusiastic headline, to the Union media the greatest immediate significance of Gettysburg was that the Army of the Potomac had finally scored a major victory against the seemingly invincible Army of Northern Virginia. After the disastrous defeats at Fredericksburg and Chancellorsville, it had been some time since the Union had won a major battle in the eastern theater. The Union media was more than ready to trumpet a victory with a sensational headline.