What they feel and what actually happened are two separate things. If you have any understanding what was going on after the Battle of the Red Ring you have to realize that point of view is an extreme oversimplification of what was going on at the time. Citing Galmar doesn't change anything either. Those are his opinions. Their appeal to you doesn't make them facts.
Lore:Wars - UESPWiki
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4E 175.
[50] Titus II splits his remaining forces into three hosts that surround the occupied Imperial City. After a long, bloody battle,
the Aldmeri army in Cyrodiil is utterly destroyed and the Imperial City recaptured. Lord Naarifin is hanged from the top of White-Gold Tower and kept alive for thirty-three days.
Despite the resounding victory, Titus II realizes that the Empire is too exhausted to continue fighting. Titus negotiates with the Thalmor and signs the White-Gold Concordat, a treaty that gives the Thalmor free reign to stamp out the worship of Talos in Tamriel, disbands the Blades, and cedes a large part of southern Hammerfell to the Aldmeri Dominion. Critics note that the terms of the Concordat are almost identical to those of the original ultimatum presented by the Thalmor prior to the war.
The lore indicates that the Empire annihilated the Aldmeri army in Cyrodill, and successfully recapture the Imperial city. They've captured their leader, Lord Naarifin, and was hanged (I assume in 1 of those human size cages) on top of the White-Gold Tower for 33 days in a symbolic way. I'm guessing they've executed him soon after his time was up. This was HUGE positive impact for the Empire. The strength and power was there. They went from getting their asses pounded by the Aldmeri in 4E 174 to getting a great victory in 4E 175. Then Titus decided, in spite of their great accomplishments of recapturing the Imperial City from the elves, that he would surrender to them by signing a treaty that allows the Thalmor free reign to arrest, imprisoned, and kill Talos worshipers. This decision of his cost him a great deal. He lost respect by many of his own peers and race, and that includes losing one of the most promising assets of Hammerfell.
While Cyrodill did sustain massive damage to their country.... At the time The empire had Hammerfell, High Rock, Skyrim and Morrowind for aid. I also believe that Black marsh and Elsweyr are part of the Empire if I'm not mistaken. You mean to tell me that the Emperor couldn't ask for an emergency assistance? I'm sure theirs a form of a draft in this fictional world that we love so much.
Yes I firmly believe that the Empire, with the help of Hammerfell, High Rock and Skyrim, can easily wipe out the Thalmor, and could've very easily win the war.
There's nothing wrong with the Empire carrying out Imperial Law by executing Ulfric at Helgen. He's not just being accused of the crime of high treason, he's indisputably guilty of it so the absence of a trial to which no one is even entitled in the Elder Scrolls universe is a complete non-issue as a trial is completely unnecessary to establish his guilt. Everyone on all sides concedes that he killed the High King and it's not as if he's going to deny that he killed Torygg. Ulfric himself never brings it up because unlike you, he's a character of the Tamriel and acts like it.
If Ralof was real he would disagree with you. He pointed out that the empire wouldn't give Ulfric a fair trial. How can you be guilty without being convicted? If he broke Imperial law shouldn't he be tried prior to execution? Doesn't he deserve to proof himself innocent by collecting witnesses and so on? Did you also notice during Battle of Windhelm after the door was secured Tullius started talking loud directly at Ulfric as he walks towards him: “"Ulfric Stormcloak! You are guilty of insurrection, murder of Imperial citizens, the assassination of King Torygg, and high treason against the Empire. It's over." Again how can Tullius say that hes guilty when he never step foot inside of an Imperial court?