So:
The Aldmeri accept a 'peace treaty', which essentially gives them control over the Empire...they have 'advisors' in the country, they are running patrols and security operations to protect 'their interests', and they are no doubt guiding the strategy of the civil war. No need for the Empire to win, because while both the Empire forces and the Stormcloaks are fighting, they are weakening themselves, and all the time the Aldmeri are sitting back either growing elsewhere or strengthening themselves.
Ultimately, this leaves two potential courses of action...The first is that the Aldmeri wait until both factions are worn out, then strike; or, Second, they declare that the Empire is unable to govern, and move in to 'protect' the civilians. Either way, it's a take over, and war.
The whole issue is that civil wars are nasty...why would the Aldmeri want to look like the bad guys, when the Empire and Stormcloaks can do that for them? Remember that the Empire was born out of someone crushing all opposition in the provinces and uniting the country under his banner and beliefs....and that sort of thing carries long lasting memories...the people of central asia still revere the warlords that rode out of the east and united them through blood and steel.
Edit:
I don't think drawing a paralell with Vietnam is particularly accurate, when the US is seen as the aggressor...you youngsters should remember that the free world (some of us) went there to fight against a communist takeover, and any examination of the politics of that will point the finger directly at the USSR and the then People's Republic (I say then, because times, policy and motivations change). I'm pretty sure that there would still be more than a few people from SEA who wish that more of our own people had supported that effort, if they had survived both the war and the takeover afterwards.