Doom's not LOLnopeing it. It's EXACTLY the kind of thing that would succeed against him. It's going to get what it wants by using Doom's overwhelming ego against him.
1. Doom is extremely vulnerable to ego-baiting. Duh.
2. Doom has never been able to resist anything that offers power.
3. The Ring isn't going to try to make Doom be nice to Richards, or kneel to Kilgrave (Purple Man, if you're asking), so Doom isn't going to really want to resist.
The Ring wouldn't have any issues at all with Doom.
And I disagree on the willpower thing - it would matter for some people, it's just that Doom is so expressly weak to the things that the Ring is going to offer him that he's really got no chance to bring his willpower to bear.
Doom wouldn't have much reason to resist the Ring's impulses.
Doom: Get more power and rule over everyone? Just another day in the castle.
“The master has failed more times than the beginner has even tried.”
-Stephen McCranie
The ring, since Doom will inevitably be following it's lead. The thing is, Doom on his own isn't going to do things that piss off people he can't handle (competently-written Thor or above, for example, who just won't care about trifles like "laws" when Doom does something stupid to someone (s)he's protecting), but under the auspices of the Ring, he almost assuredly will, eventually, and then he's getting smashed.
Doom might fall under the category of people who the ring can't really offer anything substantial to anyway
The ring is really good at promising and manipulating, it doesn't really have to have anything to offer. It just needs to convince Doom of stuff he already believes anyway (he's better than everyone else, he should be in charge, people should be forced to accept that, he should be all-powerful, blah blah blah), and then "push" him a little further along said paths then he'd want to be in any case.
Now, considering the actual scenario, Doom is waaaaaaaay beyond anything seen in ME circa LotR, so what happens is Doom basically takes over and becomes a tyrant over Middle Earth. Sauron without the ring isn't going to able to do anything to Doom's mind, as long as Doom doesn't let him, and nobody else on ME has the slightest chance. So Doom winds up ruling Middle Earth, the Nazgul become his bitches (which is good - he's gonna have trouble making Doombots and could use some servitors). Most people's lives don't get better or worse in the long term - given the leadership on ME, they are just answering to a different jack-booted jackass. Aragorn, Gandalf, Galadriel, Celeborn, Elrond, Saruman, Sauron et. al. get slaughtered in the take-over, and never get a chance to sail west.