I'll make another post since I think editing the last one would be unfair.
After reading through the auction article and looking at the sword in detail, it is, after all, a tachi. A horseback specific sword with a curve greater than later swords. It specifically states that this sword sold in the auction is an original, that never did get shortened and thus retains its size and shape. I would like to see a sword from 13th century Japan which looks similar to the one from the gameplay trailer, as that one looks very narrow like uchigatana (and is worn blade up like a uchigatana as opposed to the tachi in the screenshot on the horse which is worn blade down).
You said that, in order to fight the Mongols, swords were modified for thrusting (shorter and more narrow) so that means that swords similar to uchigatana must have existed since that is what a uchigatana is (shorter and less curved). So in the end I suppose it makes sense to have them in the game.
About the over extending blows though, I think they are mostly done for effect. It looks cooler to slice some bad guy across his neck and then keep holding your sword pointing sideways at the sky, even if it is an extremely vulnerable position. Much like all the ballerina moves in Star Wars and other martial arts movies (turning 360 and other such moves).