why i cant enter the Total War: SHOGUN 2 giveaway

Contact Steam Support. Tell them they accidentally gave you a free game and they need to delete it from your account. See what they say.

That's going to be what's causing it then, I guess.

Until Steam fix things, and allocate discrete IDs to the two games (which isn't going to happen), I guess that's it.

Nothing that can be done on Steamgifts can do to fix things.

Per my post, the BASE GAME is clearly showing on your Steam profile...

While you may not actually own the game per se, its presence in your library is almost certainly what's preventing you from entering these giveaways.

:)