I decided to read a bit about the Nine Divines, and it doesn't really seem to me as if Talos is really a god. Don't get me wrong, I'm all for the Stormcloaks being allowed to worship him as one, I just don't think he is. What do you think?

He is a divine. He can give you blessings and he has his own avatars and stuff. He's not an Aedra but he is a god.

Thanks, that question was bothering me.

Here's a few reasons besides the blessing at shrines one:
In The Elder Scrolls IV: Oblivion, the "blood of a divine" is needed to open the portal to Mankar Camoran's Paradise. The blood used is from the Armor of Tiber Septim, which implies that Tiber Septim indeed became a god.
In The Elder Scrolls IV: Knights of the Nine the Blessing of Talos is what allows the player to follow Umaril the Unfeathered into the spirit world and destroy his very soul preventing him from being reborn in oblivion and returning again. The blessing also allows the player to return to his body afterwards, further evidence of Talos' divinity.
Tiber Septim is also not to be found in Sovngarde, alongside the other Nord heroes, during the Skyrim quest Sovngarde. This may further imply the claim that he became a god.
At the end of The Elder Scrolls III: Morrowind, the player is met by an aging Imperial named Wulf, who bestows on him/her a power called "Favor of the Emperor." If Lalatia Varian is asked about this, she will tell the player that this is a manifestation of Talos; similar manifestations of Mara and Zenithar occur in the Imperial Cult quest line.

Talos is a God.

Even the Thalmor know this very well. There's no way they couldn't know.

The are denying Talos either to gain politically and to split Skyrim and the rest of the Empire, or (if you believe OOG sources) they are trying to actually undo Talos as a Divine by attacking him where he is most vulnerable: at his worshippers.

Talos is a Divine because he, in certain ways, takes the place of another god, Lorkhan, who was an Aedra. Sort of an inherited matter.