"Victory is measured in enemy territory captured and held and the destruction of the enemies ability to resist."
Not in all cases. The South didn't need to capture Kentucky or destroy the A of C, it simply had to survive.
Bragg did not "lose Kentucky". It was in Union hands already. At least he made a decent effort to regain it.
"What did the Confederacy gain?" See my first message - Chattanooga for a year.
"Hood not given up the fight and left with his army". Actually, Hood was hanging out in NW Georgia driving Sherman crazy when Sherman decided to burn Atlanta and head to Savannah.
Why was it in union hands? Because after Confederate General Leonidas Polk failed in his attempt to take Kentucky for the Confederacy. Polk ordered Gideon Pillow to occupy Columbus. The Kentucky legislature passed a resolution ordering the withdrawal of only Confederate forces. Governor Magoffin vetoed the measure, but the legislature overrode the veto. They petitioned the Federal Army for help. Grant entered Kentucky on 6 September, 1861. In addition, the General Assembly ordered the flag of the United States be flown over the Capitol in Frankfort, declaring it's allegiance with the Union.
While Confederates challenged Union control, including Forrest's and Morgan's Cavalry raids, they never succeeded in gaining control of the state. Moreover, Confederate incursions only served to help align Kentucky more strongly with the Union. Some 125,000 Kentuckians flocked to the Federal Banner as compared to 35,000 who took up with the Confederacy. On January 19, 1862, General George H. Thomas defeated Confederate forces at Mill Springs. CS Brig Gen Felix Zollicoffer was killed when he blundered into the Federal Camp in the Fog. The Confederates were forced to retreat across the Cumberland River and many of them drowned.
Following this, Edmund Kirby Smith was unable to dislodge George W. Morgan's Federals from Cumberland Gap. Bull Nelson's inexperienced troops took a licking at Richmond and Wilder surrendered at Munfordville. While tactical victories, they accomplished little else. While Bragg was bragging about defending Kentucky during the installation of a Confederate Governor, Buell's Federals descended on Frankfort and put Bragg to flight. Bragg retreated to join Smith and they abandon Kentucky. For the remainder of the war the Confederates would not, and likely could not make any effort to seize and hold Kentucky.
Meanwhile, Middle and West Tennessee were lost to the Federals. Retaining possession of Chattanooga for another year did them little good or no as Bragg managed to lose that as well. If that is your definition of a victory, so be it. It was a strategic debacle for the Confederacy.
And then there is Hood. Hood's activity in norther Georgia was little more than a nuisance. It did not interfere with Sherman's plans. Hood knew well a straightforward fight with Sherman would have not ended well. What may have stalled Sherman was the retention of Johnston, who would have defended Atlanta instead of abandoning it. Instead, Atlanta was burned and Sherman marched, virtually unopposed, to Savannah.