We only know of a few terms of the Treaty, there are probably many terms on it. The ones you listed are the big main terms which are the most disliked. The handing over Southern Hammerfell was because the Dominion already occupied it, Imperial Army couldn't continue fighting. Though the fact the Thalmor did accept peace does show a great deal. The Aldmeri Dominion lost their entire main army. Sure the Thalmor wiped out a good deal of soldiers, but the Imperial army is still standing. They didn't leave the Empire, Hammerfell was dropped as a Province, they were kicked out. Though one also must remember, 'But the Redguards should not forget the great sacrifice of Imperial blood - Breton, Nord, and Cyrodilic - at the Battle of the Red Ring that weakened the Dominion enough to allow the eventual Second Treaty of Stros M'kai in 4E 180 and the withdrawal of Aldmeri forces from Hammerfell.' - The Great War.
The Septim Empire wasn't that great, in fact they had some of the worst Emperor's known to man, their dynasty was plagued with wars, loss of Imperial authority even civil wars between the Septim bloodlines such as the War of Red Diamond. The Empire have been to Summerset Isles before yes, during the Second Era with Tiber Septim, they invaded and forced the High Elves to submit to Imperial authority. It took one hour to force the surrender of Alinor. 'Surrender of Alinor, 2E 896. Given to the Empire as a part of the terms of the Armistice by the Tribunal, Numidium besieged the capital of Summerset Isles, its fall happening within an hour. Alinor's fall marked the end of the Tiber Wars, finally unifying Tamriel, in turn leading to the proclamation of the Third Era'
The initial success of the Aldmeri Dominion forces was they had been preparing for seventy years, they were silent for seventy years before their sent their ambassador to the Imperial city. Their army flanked the Imperial defenses on Valenwood border, the success was because the Empire holds garrisons throughout each province of the Empire, it would of taken quite sometime for the Imperial army to mobilize, while the Dominion was already in force and ready to go. The Empire may of been weak prior to the Great War, but it showed the Aldmeri Domion that even a weakened Empire, could defeat the full strength of the Aldmeri Dominion who had time to plan for over seventy years, the Empire had a few days before the Dominion invaded after the terms were rejected.