Elves want to create a sort of cosmopolitan cultural denominator for all of Tamriel. It isn't about domination but peaceful coexistence. The Thalmor look back and see constant and unending agression against the elves. For example, after the Alessian rebellion and taking down slavery the Ayleids that remained, many having supported Alessia, where cleansed as a people and culture from Cyrodil. Is the initial conflict legitimate? yes, i would say so. The prosecution that followed? not so much. That is the underlying problem they see with Talos and other cultural aspects, a menace to the existence of the elves themselves. These traits advocate genocide against the elves. 

Concerning politics nothing is certain. Any of us could be correct, or not at all. 

The Dominion doesn't want to "steamroll" anybody. Their conflict is cultural, religious and political. The racial factor is not an issue for them, the emphasis on one race is. All non-man provinces already separated from the Empire before the Great War and for good reason. Talos is often described as an advocate and chief deity of the Empire before the concordat. Not smart when you want to unite different races under one banner. You must create a common ground for it, religion did this quite well until Talos. He advocates a man-centric model, all non-man races will have nothing to do with it. Meaning their objectives aren't invasion in the typical sense, the only territorial gains they wanted was the coast of Hammerfell to expand their area of influence enough to safeguard their position. History in TESO shows the Altmer as a very conservative and isolationist nation, they aren't the aggressors and don't want to be. The war and their conflict with the Empire is a response to centuries of aggression to their civilization.  Militarily speaking the Dominion has a very strong position. I very much doubt they could take out the Dominion through conventional means without uniting the other human provinces first. 

I disagree in some fundamental aspects. This was a victory for the Aldmeri Dominion on the religious, political and military dimensions.  An independent Hamerfell gave precedence to other regions wishing to be independent, creating a credibility crisis for the Empire. A crisis initiated by Black Marsh and subsequent disasters that befell Morrowind.  The war was fought mainly in Cyrodill and Hamerfell, not only many lives were lost but also the productive capabilities of these regions has been damaged quite severely i would say. With Skyrim going through a civil war, the Empire deviates resources needed for its reconstruction and it can only rely on two regions for the humongous effort: Cyrodill and High Rock. This also shows the change in strategy the Dominion has done. They understand that given time the Empire could recover, so they decided to support indirectly and directly any dissident groups and sentiments in every region it can reach. Something facilitated by the articles of the White-Gold Concordat. I wonder if the Dominion has approached House Redoran or any other faction with clear anti-imperial sentiment. Furthermore, the Dominion also has an even greater advantage over the Empire than before: positioning. With Hamerfell independent any response the Empire could have to the Dominion navy has weakened substantially. Remember the Niben is the life-line of the Empire and the Dominion can easily control it by sea and land thanks to the general strategic positioning of its forces and allies. The Dominion doesn't actually need to conquer Tamriel, they just need to split it up. Diplomacy with different smaller kingdoms is an attractive possibility as they can exercise their influence without a lot of resources and energy.   The Empire would be wise to cement as many alliances as they can get their hands on. For the elves this has just begun. 

30 years isn't enough time to recover, it's not only about having babies but also train them, create the economic structures required for professional standing armies and the creation of seasoned veterans. Certain factions of Valenwood were against the Dominion others were with the Dominion, to say Valenwood was made to adhere to the Thalmor when seeing that the Thalmor are also composed of powerful elements of Bosmeri politics and lobby's. The Khajit adhered to the Dominion willingly. Valenwood does produce food, in the form of meat, not all of Elsywer is a desert and from what i've heard the Summerset Isles are quite abundant.  The human nations didn't acquire peace after the end of the Great War, Skyrim is full with internecine conflicts as is Hammerfell, now that the Empire has relinquished its hold factions will rise and fall in their bid for power.  The dunmer are going to avoid a direct confrontation with other nations but that doesn't mean they are going to be helpless, they have ports, mines and other logistical and natural resources that could aid any side they would choose to help. Even if they stay out of it and remain independent, where they to shun both Dominion and Empire the one to be most affected by it would be the Empire.  The Dominion is indeed very capable from a diplomatic standpoint, gaining the alliance of the Khaijit and certain power groups in Valenwood, not only that they tried to force the Empire to go to the negotiating table after taking the white-gold tower, or the pact they made with the Redguards. This shows that the Dominion uses war as a means and not as an end in itself, basing their legitimacy on basis of the law. Something the Empire founded by Tiber Septim also did but are failing at the diplomatic and political game lately. Just with one pact, Skyrim is at war with itself and Hammerfell got separated. The Dominion is playing it smart, they have committed some errors but they learn from them and fast. Seeing how the Thalmor plan in advance with such level of detail and knowledge, they have already planned for the next steps in the game. Not saying the Empire doesn't have its strengths and resources but wars are won wilth the mind not with brawn (a focus pro-imperials have in general). Just a bit of advice to the Empire, the Dominion underestimated you to a certain point, don't return the favour if you want to win.