But, how can they possibly not recognize Talos as a God? In the real world, the legitimacy of a deity is mostly the subject of faith. Any actual evidence of a god's existence is mostly restricted to ancient texts and the accounts of supposed witnesses.
However, in Tamriel, the Gods are active, known public figures. They directly involve themselves in the mortal world. You go and pray at their altars, and you immediately get a real, tangible, direct material benefit. Sometimes, the Gods will even directly speak to mortals, giving weapons, armor, and reusable soul gems as rewards for favors.
In Oblivion, there was a popular user mod called "The Lost Spires," and one of the archeologists in that mod was curious about this ancient culture who worshiped some Gods, despite there being no proof that those Gods even existed. In other words, since the existence of gods in this universe are just as much a physically observable phenomenon as my sword in your face, the actual lack of such evidence is genuinely startling.
With Talos, we have just as much observable confirmation of his divinity as we do with any other Tamrielic god. Go and pray at his altar, and you get a temporary reduction in Thu'um recharge time. You can get all your diseases cured by praying there, just like with any other shrine of the original Eight Divines. Two hundred years ago, Martin Septim was able to obtain the "essence" of an Aedra by using Talos' blood, something that would only be possible if Talos was, in fact, an Aedra.
So... how is it that the Thalmor don't recognize Talos as a God? Are they really so arrogant that they can't see two feet in front of them and see that proof of his divinity literally litters Tamriel?