Screwing over both sides does not help Hammerfell in the slightest.
But...but screwing both sides over doesn't help anybody but the Thalmor! Are you now or have you ever been a dirty, stinking, milk-drinking Thalmorist?!
Ah, you only think that. By screwing over both sides, I have weakened both sides which the Thalmor want. HOWEVER, it continues to keep the Empire occupied, allowing Hammerfell to develop its strength to prevent the Empire ever saying "look, my army is still bigger and more powerful than yours. You should be a part of me again, even though I abandoned you." It will also keep Skyrim distracted long enough for Hammerfell to finally retake territory lost during the War of Bend'r-Mahk. It also helps to delight the Thalmor who will think "this is perfect! Everything is going according to plan!" which keeps them focused on Skyrim when they should be starting to worry about a more unified Hammerfell that absolutely hates them.
The lore establishes that during the War, the Crowns and Forebears actually helped each other and Hammerfell is rather unified. By keeping the Empire and Stormcloaks occupied, we also accomplish the goal of keeping the Thalmor distracted while we continue to prepare for an inevitable future conflict. Essentially, we're trying to keep the fight going to the delight of the Thalmor who fail to notice that we're approaching their backsides with our daggers drawn.
Also, considering this character tossed Elenwen out of the negotiation, routinely kills Thalmor Justiciars, assaulted Northwatch Keep with a band of Nords, and raided the Thalmor Embassy, I'm fairly certain he's not a Thalmor-sympathizer.
