I recently watched Game of Thrones. The show is set in a pseudo-medieval world. I'm wondering whether the sword fights and the swords are authentic representations.
Here're an example:
Not particularly. While it is, in part, derived from European sword fighting, there are also dashes of Chinese sword theatrics (Wushu) along with exaggerated and dramatic moves designed to film well. As with hand-to-hand martial arts, actual real life fighting is a lot faster, direct and brutal. The downside is that these methods don't film well.
It is worth bearing in mind that single handed swords did little against plate armour, they did little against maille and padding unless you landed a good solid thrust. Curved swords have almost no affect against solid armour too.
I have suits of maille and plate and regualarly fight in tournaments wearing them. We have fought at full power with swords and I have never been hurt despite getting hit a lot!
The fight with Ned Stark and Jamie which the OP has provided a link for is a good example of Hollywood fighting. If you watch carefully the head shots and thrusts would normally miss even if the target stayed still but they move or block and with a good camera angle it looks like a close thing but they were never in danger. Slashes to the body are normally swung in when the opposing blade is already in place to block them.
I just watched the scene with Jamie and Briene on the bridge. The part just before the actual sword clashes is historically correct as related to 15c fighting manuals. They are taking recognised 15c guards called the ox and the plough. Once the fighting starts the blows are telegraphed and aimed at the weapon rather than the person. There is also a lot more pressing swords together (called binding) than would normally happen for real, if you pressed swords and stood that close you would be punched or headbutted. Jamie mentions that she should not grimace before thrusting, this is correct and is actually a very common bad habit with newer fighters.
Historically accurate as compared to what? Game of Thrones is a fantasy, not based on history or any historical period, so there is no basis for comparing it to a historical event like the Battle of Hastings, for example. The story, and the style of fighting, is in the minds of the show's creators.